Physiological Responses to Shifting

Bargaining Power: Micro-Foundations of

Commitment Problems1

Dustin Tingley2 Jooa Julia Lee3 Jonathan Renshon4

This draft: September 28, 2014

1We are especially grateful to Ariya Hagh, and the team at the Harvard Decision Science Lab-

oratory for facilitating this research, including Judith Ezike, Dan Zangri, Nicole Ludmir, Gabe

Mansur, Roseanne McManus, Jeanie Nguyen, Jakob Schneider, Phil Esterman, Claire Tan, Will

Boning, Carolyn Killea, Amee Xu, Jack Schultz, Sarah Sussman and Mark Edington. Tingley

thanks Harvard’s Weatherhead Center for International Affairs and Institute for Quantitative

Social Science for financial support. We thank Josh Kertzer, Rose McDermott, Paul Poast,

Alex Peysakhovich, Yunkyu Sohn, Jessica Weeks, and the UCSD Behavioral International Rela-

tions workshop organizers, especially David Victor, for their thoughtful comments on previous

versions of this paper.2Government Department, Harvard University, Cambridge, MA 02138. Email: dting-

ley@gov.harvard.edu, URL: scholar.harvard.edu/dtingley3PhD Candidate, Harvard Kennedy School. Email: jooajulialee@fas.harvard.edu, URL:

http://scholar.harvard.edu/jooajulialee4Assistant Professor, Department of Political Science, University of Wisconsin-Madison.

Email: renshon@wisc.edu, URL: http://jonathanrenshon.net

Abstract

Commitment problems are often regarded as one of the most important, and common,

causes of international conflict. IR work on the subject suggests that, at the micro-

level, shifting bargaining power can generate an incentive to reject offers, and thus lead

to a costly conflict that destroys resources. Despite this, there is a noticeable gap in

our understanding of how commitment problems change individual behavior in actual

bargaining. We use a novel experimental protocol to study how individuals react to

changes in bargaining power in a game where bargaining power is operationalized as

the probability of winning all the resources. We use a psycho-physiological measure–

skin conductance–in order to assess individuals’ reactions to bargaining. We find that i)

people are more likely to reject offers when they expect the opponent’s bargaining power

to increase (and hence support for a key pillar in IR theory). We also find, only in the

presence of a large shift in power: ii) higher (i.e., better) offers lead to less arousal, and

iii) higher physiological arousal decreases rejection decisions, perhaps due to an increase

in ‘aversive’ physiological arousal and the resultant difficulties in making “strategically

optimal” decisions. Our novel findings suggest that when individuals face large power

shifts, arousal may allow more intuitive decision-making and less backward induction.

This suggests that under certain circumstances, emotionally-aroused individuals are less

prone to commitment problems.

Given that conflict is costly and destroys resources, why does it occur? More than

any other, it is this foundational question that lies at the heart of the scientific study

of international relations. Given its prominence, scores of explanations have been posed

over the years. One of the most promising class of theories are rationalist accounts of

wars, which frequently turn on the presence of a commitment problem or incomplete

information. One mechanism in particular–commitment problems–has had an enormous

influence on the study of international conflict and is often argued to be fundamental to

understanding the breakdown of peace.

Commitment problems arise because shifts in bargaining strength generate incentives

in the future to renege on current commitments. For example, if country i is increasing

in strength relative to country j, country i will find it difficult to “credibly commit” to

not taking advantage of j in the future. With this in mind, the actor whose power is

declining prefers conflict while they have a bargaining advantage rather than a peace-

ful resolution that may leave them open to predation in the future. Due to liquidity

constraints, bargainers cannot prevent their opponents from being concerned about such

adverse shifts. This can lead to conflict despite the fact that it is costly (Fearon, 1995,

2004; Powell, 2006).1 Thus, future changes in bargaining power have been used to explain

preventive war, whereby a declining state chooses to wage a war against the opponent to

take advantage of its bargaining advantages (Fearon, 1995). In this paper we develop and

test for the role of emotions in a stylized decision-making context where there are shifts

in bargaining power over time. In doing so we try to push for a greater integration of

cognitive and affective forces in decision-making.

In recent years the international relations literature has seen a proliferation of work

studying the behavioral foundations of bargaining, drawing heavily on experimental meth-

ods that have human subjects bargaining over resources or responding to hypothetical

1Incomplete information explanations shift the focus to how the anarchic international environment

prevents bargainers from revealing their true valuation for a war outcome (Fearon, 1995). This type of

explanation for conflict has been studied using experimental methods elsewhere (Tingley and Wang, 2010).

The role of commitment problems in other settings is also well developed theoretically and empirically

with observational data (Greif et al., 1994; Simmons, 1994; Simmons and Danner, 2010).

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crisis simulations (e.g., Tingley, 2011; Butler et al., 2007; Tingley and Walter, 2011b,a;

Tingley and Wang, 2010; Tomz, 2007). For example, Tingley (2011) and McBride and

Skaperdas (2012) examine how changes in the likelihood of future bargaining–the “shadow

of the future”–influence the extent to which commitment problems create conflict. Quek

(2012) presents a design where offers are either allowed to change or not in the future

following shifts in power. There has also been some recent work by international rela-

tions scholars that focus at an even greater depth by examining biological variables in

experimental bargaining environments (McDermott et al., 2007, 2009; Rosen, 2005).

We innovate by tying biological and physiological factors in to a behavioral game

which IR scholars will recognize as approximating the conditions that we typically as-

sociate with commitment problems. And while emotions have become a more common

object of study in IR (see, e.g., Crawford, 2000; Bleiker and Hutchison, 2008; Mercer,

2006, 2010), we present the first work of which we are aware to use emotional arousal (as

measured by physiological arousal) as a window into System I and II (automatic versus

reflective, intuitive versus thoughtful) decision-making.

This is important because intuitive, reflexive reactions play a greater role in IR than

it is perhaps comfortable to acknowledge. While firsthand accounts of crisis situations

often emphasize the emotions of leaders and their impact on the decision process, they

are often overlooked as a factor in IR theory. For every instance in which a leader (such

as JFK on October 16, 1962) “masters his emotions” (or at least is perceived as doing

so, see White, 1992) and makes the transition from the initial emotional reaction to a

more carefully considered strategic plan, there are others in which the initial reaction

dominates, such as in Roosevelt’s “emotional reaction” to the Munich Crisis (Farnham,

1992, 229). We refrain from value judgments concerning automatic versus deliberative

processing, as both can be useful given the proper context (Gigerenzer, 2007; Gigerenzer

and Gaissmaier, 2011), but simply note that understanding how they interact with one

another in the context of bargaining over resources is likely to be helpful in broadening

our understanding of international relations and conflict decision-making.

Drawing on a body of research that has identified a critical link between emotionally-

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activated processes and intuitive decision-making (Epstein et al., 1996; Dane and Pratt,

2007), we investigate both affective and cognitive mechanisms that drive individual be-

havior in bargaining. Put more succinctly: while Welch (2003) argues that emotion can

be a “barrier to good judgment” in foreign policy, we provide evidence on the specific

mechanism by which emotions and physiological arousal tamper with our ability to make

strategically optimal decisions. By closely tracking the level of emotional arousal, we also

indirectly measure the extent to which subjects engage in intuitive (versus deliberative)

decision-making. This is accomplished via the measurement of electrodermal activities, a

physiological measure of arousal in the autonomic nervous system, which we describe in

more detail below. This allows us to measure participants’ sympathetic nervous system

activation free from any potentially disruptive social-masking or impression-management

effects and in a more direct manner than survey-based measures of emotion.

Using this novel method, we ask two broad questions in this paper. First, how does

the size of the power shift (large or small) affect how individual decision makers respond?

Second, what is the physiological mechanism that governs the reaction of individuals to

offers when a power shift is imminent? More specifically, when do offers trigger a certain

type of processing style, one that is intuitive and affect-laden, and what impact does this

have on bargaining outcomes? In order to examine these questions, we extend a recently-

developed experimental protocol (Tingley, 2011), that allows us to measure the impact of

shifting power – large and small power shifts, operationalized by the extent to which the

power each player holds differs –in a two-stage bargaining game. Our interest here is in

players’ decisions when confronted with conditions of shifting power; do they choose war

in the first round, or accept their opponents’ offers and play the second round under less

favorable conditions? Importantly, while war is typically seen as irrational because, ex

post, it makes both parties worse off, with shifting power, our model demonstrates that

rejecting offers (choosing war) is strategically optimal when the balance of power is about

to shift in your opponent’s favor.

We find that larger power shifts do in fact lead to higher probabilities of choosing

war (rejecting offers) in the first round; individuals are “taking their chances” before the

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power balance turns against them. This fits very well with the standard explanations of

preventive military action in which declining powers prefer to take a gamble now rather

than face a steep decline relative to their adversaries. However, controlling for offer size,

we find that increased emotional arousal (higher skin conductance) led to a lower level of

offer rejection in the large power shift condition, but not the small power shift condition.

We interpret this finding in light of the dual-process model of cognition, which suggests

that what we call “aversive arousal” is tampering with the ability of those bargaining

to act in a strategically-optimal manner. This particular finding suggests that emotional

arousal does not necessarily lead to less optimal, inefficient outcomes, but may actually

run counter to decisions to engage in costly conflict. We also run a follow up experiment

where we allow for large shifts in power, but no changes in offer from the first period to

the next, such as what an institutional solution to commitment problems might do. Here,

as we predict, the role of arousal is also eliminated just as in the condition with small

shifts in power.

The paper is organized as follows. We provide a model of commitment problems in

Section 1.1 and then follow that in Section 2 with an explanation of how emotions are

likely to enter into the decision process, both in IR as well as in the context of bargaining

models and games. Section 3 outlines the design of the experiment, while Section 4

outlines our main findings related to physiological arousal and bargaining, as well as a

follow-up experiment in Section 5 that used an alternative experimental manipulation.

Section 6 concludes.

1 Bargaining, Shifting Power and Physiological Arousal

Commitment problems have gained traction as one of the more powerful explanations

of conflict in the study of international relations. They are part of a body of literature

that identify “mechanisms” that lead to conflict. In the sense the term is most often

employed, “mechanisms” denote a set of utility maximization assumptions and a partic-

ular bargaining environment that result in particular predictions about when conflict will

occur. However, they do not offer any guidance on how individual decision-makers might

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be affected by these dynamics, nor how they are likely to respond. This is a critical next

step in understanding the dynamics of international conflict, just as study of micro-level

behaviors has furthered the study of strategic choice in other domains (Ostrom, 1998;

Camerer, 2011). In this section, we first present the basic intuitions of a model of com-

mitment problem dynamics, and then highlight how these dynamics might operate at the

individual level.

1.1 A Model of Commitment Problems

The intuition behind this type of bargaining model of conflict is as follows2: There are

two decision makers from competing countries (Antigua and Brazil, or more generally,

A and B) and two periods (present and future). In each period, Antigua makes Brazil

an offer to divide resource that has a value of 1. In the first period, Antigua makes a

demand to Brazil. If that demand is accepted, then the game continues in the second

period (the future) and Antigua again makes a demand. As before, if Brazil accepts the

demand, the resource is divided in the specified manner and the game ends. If in the

first period, Brazil rejects the demand, then both players/countries play a war lottery, in

which one player wins the resource (with probability p) but both players pay some costs

(since war destroys some of the value of the stake). If a “war” is fought in the first period,

then the winner automatically gets the whole resource in Period 2 as well (the future). If

Antigua’s offer is rejected in the second round, then (as before) both states play a war

lottery to determine who wins the resource (less the costs of the war).

The key question in this model is: what will make Brazil reject the offer (i.e., choose

war) in the first period? As noted by many IR scholars (rationalist and non-rationalist

alike), shifting balances of power (and in particular, the expectation of shifting power)

are likely to change both states’ calculations. If Antigua’s power is increasing relative to

Brazil’s, then a commitment problem dynamic exists, since there is no way for Antigua

to credibly commit to not taking advantage of Brazil in Period 2 (by demanding most

or all of the resource). We can operationalize this shifting power dynamic by increasing

the probability of Antigua’s victory in Period 2. If this dynamic holds, one would expect

2We provide a more detailed exposition of this model in Appendix A.

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Brazil to make the strategical optimal decision to choose war (i.e., reject Antigua’s offer)

in the first period, since doing so allows it to take its chances with a war lottery before

the power dynamic has shifted in favor of its adversary. This is the logic of preventive

war.

If, on the other hand, both states expect the power balance to remain stable across

periods, we wouldn’t expect the dilemma posed by commitment problems to be as severe,

and hence expect to see fewer instances of preventive war. In the studies described in

this paper, we “switch on” the commitment problem dynamic by allowing A’s probability

of winning to increase over the two periods of the game. We also present a follow up

experiment inspired by Quek (2012) which allows for a large shift in power, but no ability

to change offers in the second period; that is, A actually can credibly commit to not

taking advantage of its adversary in the future.

Notice that this model does not offer mechanisms particular to the human decision-

makers that are ultimately of interest. To see this clearly, consider the contrast between

the pioneering work in behavioral economics that seeks to understand the physiological

bases of strategic choice versus simply relying on the abstract choice models themselves

(for brief review see Camerer 2003a, chapter 2). What physiological mechanisms operate

when people face situations with commitment problems? Do individuals calmly calculate

the prospects for conflict and respond accordingly, or do automatic, emotional processes

become involved?

In the following section, we attempt to complement the model describe above and

remedy some of the issues common to the study of these processes in IR. While emotions,

stress and physiological arousal have long been implicated in narratives of foreign policy

decision-making, we provide causal evidence on their role through the use of experimen-

tal methods. And while many schools of IR ignore the individual entirely, we bring the

individual back into rationalist theories of war. Parallel with other literatures in political

science using a novel method in psychophysiology (e.g., Oxley et al., 2008), we study the

physiological bases of bargaining in situations where commitment problems are present.

To that end, we set up our experiments to test not only key propositions well-known in

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the commitment problem literature (e.g., the impact of power shifts on commitment prob-

lems), but additional individual-level theories that describe the physiological mechanisms

through which those power shifts exert their influence.

2 Emotions in Conflict Decision-Making

Our research design, described in the next section, allows us to examine the effects of

physiological arousal within the specific context of bargaining under the shadow of shift-

ing power. But the inspiration for the study is far broader. In fact, the question of

whether and how emotions and intuition affect political decision-making is a long-standing

puzzle in IR. Because of the obvious and inherent difficulties in “proving” that physio-

logical arousal, emotions or intuition can explain behavior in any given circumstance,

what we are left with is mostly speculation. Nevertheless, the speculation is intriguing,

as emotions are implicated strongly in a wide variety of contexts, from shifting leaders’

reference points (Farnham, 1994) and helping them interpret what would otherwise be

overwhelming amounts of information (Mercer, 2013) to general theories of international

war (Thayer, 2004; Cashman, 2013) and crises (Gordon and Arian, 2001; Winter, 2007).

Our goal in this paper is to provide micro-foundations that shed light on this elusive

phenomenon, but before we do so, we present several illustrative examples of what ways

in which emotions and intuition are commonly implicated in international politics.

One class of decisions in which emotions, intuition and arousal are commonly impli-

cated are those in which leaders react to new and surprising information. For example,

upon learning that the Soviets had installed missiles in Cuba, President Kennedy (quoted

in Allison, 1969, 713) famously exclaimed, “He can’t do that to me!” Less better known

is the quote of his brother Robert, “Oh shit! Shit! Shit! Those sons of bitches Russians”

(quoted in Stern, 2005, 22). More recently, virtually all members of the Bush administra-

tion had what were described as emotional reactions upon hearing of the terrorist attacks

on 9/11. President Bush’s was perhaps the most obvious, as he cried on television in

the Oval Office and “choked up” in Cabinet meetings in the days following the attack

(Woodward, 2002).

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But surprise is not a necessary precondition for emotions to play a role in international

conflict. In other cases, the stress of a long, drawn-out conflict can wear leaders down.

During the Iranian Hostage crisis, President Carter went through several emotional stages,

from “elation” upon learning that Iranian President Banisdar had offered a deal to return

the hostages, to bitterness and anger when the deal failed to materialize (Harris, 2004). In

one of the interesting aspects of the historiography of the crisis, the dispute between Carter

and Cyrus Vance (who resigned following Carter’s decision) devolved for many years into

a war where each side attempted to pin the other as “emotionally overwrought” (see

discussion in Glad, 1989). Emotions have also been frequently invoked in explaining Israeli

decision-making during the Yom Kippur War. During those few days in 1973, Moshe

Dayan appeared to have an emotional breakdown, “frequently” repeating the phrase “the

‘Third Temple’ is under threat” (implying that the existence of Israel was threatened) and

crying while exclaiming that “everything was lost” (Bar-Joseph and McDermott, 2008).

Even wars and crises are not necessary for emotions to be implicated in critical ways

in explaining international politics. The feeling of injustice, for example, can trigger

powerful emotions, as traced by Welch (1995) through many long-standing rivalries in

world politics. And to return to the Cuban Missile Crisis, but approach it from a different

perspective, emotions have been strongly implicated on the Soviet side. In fact, all the

recent evidence we have points to a strong role of emotion and intuition in Khrushchev’s

decision to send missiles to Cuba in the first place. Taubman (2003) paints him as

a resentful figure, convinced that U.S. nuclear policy was “particularly arrogant” and

quoted as saying that “It’s high time their long arms were cut shorter.” Lebow (1990,

490), too, describes Khrushchev as “acting out of anger” in his decision to install missiles

in Cuba.

The above paragraphs provide a brief illustration of the ways in which emotions are

implicated in international relations, but three key issues are readily apparent. First,

in the literature in which emotions are explicitly called upon to help explain outcomes,

little evidence is provided for any causal role. Leaders may indeed have appeared to

have emotional breakdowns (as was the case for Moshe Dayan in 1973), but even if we

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grant that basic fact (which also requires a leap of faith given the difficulty in imputing

emotions to others, incentives to misrepresent, etc.), it is far more difficult to argue

that this caused any particular even to occur. While statesmen typically overestimate

the influence of individuals, political scientists are justifiably skeptical that individual

reactions are anything more than noise distracting us from the larger, structural forces at

work. For example, even if Khrushchev had an emotional reaction to the strategic balance

in 1962 and shortly thereafter ordered the missiles delivered to Cuba, it is difficult to argue

that taking the emotion out of the situation would have changed anything; after all, the

balance of capabilities would still have been in the U.S.’s favor and Khrushchev had long

seen ICBMs as a shortcut to strategic parity.

But while the literature that draws upon emotions and intuition in decision-making

often relies upon speculation in making causal arguments, entire other schools of work

have left the individual–including their physiological reactions, emotions and intuition–out

of the picture entirely. Rationalist work is a primary example of this pattern. Ultimately,

rationalist explanations for international conflict must stand up to empirical testing, and

experimental methods provide one promising avenue for testing out the mechanisms drawn

from formal models (McDermott, 2002). In doing so, however, it would be a mistake to

waste the opportunity to derive additional implications at the individual level to test in

combination with the insights derived from models. These additional insights can help

provide additional information about the mechanisms through which larger, impersonal

forces work.

Finally, there is little general understanding of effects of emotions. The conventional

wisdom for many years was a version of emotion that was opposed to reason. Thankfully,

this straw-man has largely been put to rest (e.g., in McDermott, 2004). However, the

realization that emotions are neither inherently beneficial nor detrimental in their impli-

cations for decision-making has exposed a large gap in our collective knowledge. We lack

well-established theories and empirical foundations for understanding how emotions affect

outcomes of interest to international relations scholars (see Renshon and Lerner 2012).

This has left us largely in the dark on crucial questions such as whether and how emotions

9

might be incorporated into traditional theories of international relations, as well as under

what circumstances this is likely to have positive or negative consequences. In the next

section, we show how dual-process theory provides us leverage in examine the effects of

emotions in our bargaining experiment.

2.1 Dual Process Theory: A Window into Emotions in IR

To help address some of these shortcomings with respect to the study of emotions in

IR, we turn to dual-process theory. The idea that individuals’ cognitive processing can

be described as two parallel systems can be traced back at least as far as James (1890)

and Freud (1900), who described a dual system of “rational” and “irrational’ thinking.3

We follow Evans and Over (1996) in conceptualizing two parallel cognitive processes,

System I and System II (see also Kahneman 2011). The former is based upon previous

experiences and beliefs. It is characterized as “implicit, associative, fast and highly robust

(Gilinsky and Judd, 1994).” Perhaps most importantly, it is automatic: it occurs all the

time without our awareness. In contrast, System II is slow, controllable and explicit (in

the sense that one is consciously engaging in the act of analytical reasoning).

Emotions tend to be more closely associated with System I processing. That is, indi-

viduals seem to feel an emotion, and then construct a rational edifice around that feeling

in order to explain why they are angry/sad/happy/etc. (Haidt, 2001). In some cases,

emotions are explicitly linked to System I processing (Epstein, 1994; Hassin et al., 2004;

Evans, 2008), while in others, evidence is provided based on the parts of the brain involved

in both emotion-processing and System I processes (Lieberman, 2003). That emotions

are so strongly associated with System I processing is of immense help empirically, as we

are on firmer ground in measuring the generalized physiological arousal associated with

System I than we are in targeting specific emotions (Myers and Tingley, 2012).

The question we pose in this paper is: how do these different processing styles affect

bargaining? In non-political contexts, there is a substantial amount of research on the

benefits of System I processing (Plessner et al., 2007; Gigerenzer, 2007; Gigerenzer and

3For more detailed history of dual-process frameworks, see Osman (2004). For an overview of some of

the controversy associated with the framework, see Gigerenzer and Regier (1996).

10

Gaissmaier, 2011). In IR contexts, however, it is far more rare for scholars to make

the argument that the affect-laden System I processing is beneficial in terms of avoiding

conflict. One notable exception is Blight (1992), who argued that the fear experienced by

U.S. leaders at the height of the Cuban Missile Crisis was adaptive in aiding their careful

navigation of the crisis. A more theoretical treatment offered by McDermott (2004) makes

the important point that emotional processing is not definitionally opposed to rationality,

and in fact can be a key component of making strategically optimal decisions. However, an

underlying assumption of much of IR (and social science more generally) is that “logical,

rational calculation forms the basis of sound decisions” (McDermott, 2004, 691). Because

there is so little empirical research on this question, however, below we explain the ways

in which processing styles may affect political decision-making, and then draw hypotheses

from related behavioral work on bargaining.

The first, and most obvious way that processing style might have an affect on decision-

making is that political leaders might act on their initial, emotional reaction to a situation.

In high-pressure, time sensitive crises, there may simply not be very much time for re-

flection or deliberation. Emblematic of this is the “explosive reaction” of Kissinger and

Nixon to Syrian intervention in Jordan in 1970 (Dowty, 1984, 153).4 And in general, the

time pressure associated with intense crises seems to exacerbate the influence of emotions

(Crawford, 2000).

However, even if there is abundant time to reassess the situation and deliberate

over options, the initial automatic response may quite important. What Holsti (1970)

termed the “definition of the situation” and what psychologists refer to as “framing”

may exert tremendous influence over how the situation is handled even after reflection

(Levy, 1996; Mintz and Redd, 2003). The reason for this is two-fold, as even in longer

time frames, it is often the case that some options are discarded immediately (DeRouen

and Sprecher, 2004; Mintz, 2004), so that initial reactions may have far-reaching effects

even if the remaining options are considered carefully. Further, ways of understanding

4Nixon later recalled “they’re testing us...The testing was continuing, moving a few notches higher

each time. We would have to decide what to do very soon, or it might be too late to do anything (Dowty,

1984, 153).”

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what is happening are often framed around analogies and metaphors that are chosen

instinctively (Khong, 1992; Shimko, 1994). If we return to the well-trod territory of the

Cuban Missile Crisis, one notices that even though Kennedy is often congratulated by

scholars for engaging in a thorough, deliberative decision-making process (following his

initial, emotional reaction), the basic premises of the crisis –particularly, that it was a

crisis– were settled on instinctively and never once challenged.5

As is evident, there is substantial anecdotal evidence to suggest that processing style

and emotions may impact conflict decision-making, but very little in the way of system-

atic evidence. Below, we turn to the behavioral literature on experimental bargaining to

provide some insight into how the dual-process model model may shed light on bargaining

decisions.

2.1.1 Micro-Level Studies of Bargain, Arousal and Intuitive Judgments

Behavioral investigations of bargaining have typically focused on the “ultimatum game

(UG).” In the UG, one person proposes a division of a resource to a second person. If

the second person accepts, then the resources is divided in the agreed upon manner; if

the responder rejects the offer then neither person gets anything. Thus, the responder

is always better off accepting as long as the offer > 0. Or, in other words, the standard

equilibrium analysis of the UG is that there should never be rejected offers, even when

they are arbitrarily low.

Initial evidence from the UG suggests that emotions play a powerful role, despite

assumptions that strategic thinking –“cold calculation” –should dominate. Blount (1995)

used a variant of the UG to show that unfair offers by the proposers can evoke anger in

responders when the allocation was intentional, but not when it was randomly generated.

Pillutla and Murnighan (1996) also found that responders who have full information about

the total endowment available to the proposer rejected more than those who did not have

any information. In other words, emotions like anger can be triggered under certain

5And, of course, the question of whether Kennedy actually “kept his emotions in check” is not yet

settled. See Lebow (1990).

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circumstances, but there is a logic to how this process occurs; a “bad” offer by itself is

not enough to trigger anger. There must be some knowledge of the motivation behind

the allocation (to know whether there was an intent to be provocative or threatening) or

a larger understanding of the amount available to the proposer (to know if the allocation

was fair).

Advances in neurophysiology have supported these findings. Sanfey et al. (2003) used

functional neuroimaging to record the brain activity of responders who were faced with

different distribution of allocations. They observed that low offers resulted in a higher

level of activation in bilateral anterior insula, an area of the brain associated with negative

emotional arousal. The intensity of activation in this region was significantly correlated

with the extent to which the offers were low, and thus led to a higher probability of re-

jection (which is the non-equilibrium response). Van’t Wout et al. (2006) and Civai et al.

(2010) similarly observed increased electrodermal activity (skin conductance), which is

associated with insula activity, when responders received unfair offers. The relationship

between offer size, physiological arousal, and probability of rejection was consistent across

these studies. Drawing from this research, we hypothesize that lower offers in our bar-

gaining game (despite its difference set-up from the traditional UG) should trigger greater

physiological arousal than high offers. p However, the impact of physiological arousal on

the act of rejection is less clear in the current study, which differs from the traditional

UG in significant ways. In previous UG studies higher offers led to less arousal, and lower

arousal levels led to less rejections. Hence lower arousal is associated with equilibrium

predictions.

In contrast, our game involves two stages, in contrast to the traditional ultimatum

game set-up in which actors face a “one-shot” choice. Simply put, the game we investigate

is dramatically more familiar to international relations scholars than the ultimatum game.

Unlike the standard ultimatum game (in which rejection leads to both players receiving

0), the responder’s rejection leads to a gamble where one of the players receives all of

the resources. This mimics the observation that war (rejected offers) does not destroy all

resources (as in the ultimatum game) and that one country can often prevail. Furthermore,

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as we describe next, the game has a repeated component that captures shifts in power,

which is absent from the ultimatum game. In the declining power condition, the responder

wins all of the resources with a probability of .7 in Round 1 and .3 in Round 2 (the

probabilities are reversed for the proposer, who wins with a probability of .3 in Round 1

and .7 in Round 2). In the control condition, the probability of winning stays at roughly

.5 for both rounds (responder wins with probability .55 in Round 1 and .45 in Round 2).

In other words, in the declining power condition, both parties know that the proposer will

be gaining power in the second round, and the responder will be losing power. Given this

knowledge, the rational course of action for the responder is to reject any initial offer and

take their chances in a costly lottery in Round 1, when they still enjoy a power advantage.

Responders in the declining power condition should, if motivated by self-interest and using

rational tools of backwards induction, reject all offers, even high ones.

Given these differences to the UG, what role should we expect arousal to play? Phys-

iological arousal may tamper with a more deliberate, cognitive processes of strategic

thinking. According to the dual-process framework (Kahneman, 2003; Sloman, 1996),

decisions are made by the interaction of intuitive and reflective processes. Physiological

arousal may give rise to more intuitive decision-making, which is associated with fast,

automatic, and effortless processing (Lambourne and Tomporowski, 2010). On the other

hand, the absence of physiological arousal would allow more reflective decision-making,

which is associated with slow, effortful, and deliberate processing.6 Deliberative process-

ing has been associated with greater equilibrium play, which in the shifting power condi-

tion would mean higher rejection rates. Hence physiological arousal may not necessarily

lead to high rejection rates in all circumstances.

To see this explicitly, in our bargaining game, the presence of large power shifts implies

that the responder’s dominant strategy is reject any offers in Round 1. Put simply, the

responder’s chances in Round 1 will always be better than in Round 2 under conditions

of declining power. Choosing this strategy requires the ability to look ahead and induct

6A good example of both intuitive and reflective processes in the ultimatum game can be found in

the work of Grimm and Mengel (2011), who found that time delays allowed more deliberation, and thus

decreased rejection rates.

14

backwards, but as Camerer (2003b) argues, people’s ability to engage in such strategic,

iterated thinking is limited. We thus predicted that responders with lower physiological

arousal should be more likely to reject Round 1 offers since their ability to engage in

reflective processing would not be impaired (compared to those with higher physiological

arousal). On the other hand, we predict that high physiological arousal should interfere

with this process of strategic thinking, which requires sufficient cognitive resources to

think about the implications of the shifting power dynamics that they will face in Round

2.

An alternative view could be that, again controlling for offer size, the effect of phys-

iological arousal on rejection decisions is positive. This would imply that individuals

with high arousal will be more likely to reject offers. This might occur because they are

tempted to reject based on spite, or some other fairness based consideration. There is

some preliminary evidence that physiological arousal is associated with the destruction

of shared resources in bargaining games (Ben-Shakhar et al., 2007), though the setup of

these games is noticeably different than the current paper (in the current work, rejection is

actually the strategically optimal choice, so to the extent that emotionally-aroused players

reject in our game, they would be doing the “right thing for the wrong reasons”). In this

story, the cognitive side (low arousal) of the dual systems approach might suggest lower

rejection rates because higher offers might be considered signals of intents to reciprocate.

We feel this story has less of a theoretical foundation, but our experiment can nonetheless

provide a test.

Taken together, we hypothesize that the size of offers will predict rejection rates,

and this relationship will be explained by the responder’s physiological arousal, measured

by skin conductance. More specifically, we expect that skin conductance reactivity will

mediate the relationship between high offers and higher rejection rates.

2.2 Hypotheses

Based on the previous discussion we have several hypotheses. First is the basic hypothesis

from the game theoretic model that when there is a larger power shift then we should see

more rejected offers. We operationalize this by investigating whether for any given offer

15

there will be a higher probability it is rejected when there is a large power shift (Tingley,

2011).

Hypothesis 1: When there is a large power shift, for any proposed division (offer size),

the probability of rejection will be higher.

The second hypothesis concerns the effect of offers on skin conductance. Following

previous work, we expect that low offers will lead to higher levels of physiological arousal,

but only in the presence of a large power shift. This follows from the logic that the

presence of a shifting power dynamic is likely to make lower offers more psychologically

salient, and aversive, than in conditions where conditions remain stable across periods. In

other words, the proposer’s lower offer in Round 1 would be interpreted as more threat-

ening and challenging to the responder, knowing that the proposer will be able to take

advantage of increased bargaining power in the next round. On the other hand, small

shifts may not activate the same aversive physiological responses against the low offer, as

the responder is not as likely to be concerned with future bargaining, but may be more

concerned with the cost of rejection.

Hypothesis 2: When there is a large power shift, low offers should be associated with

higher skin conductance. This relationship is likely to be attenuated or muted under

conditions in which power conditions remain stable across periods.

Our final hypothesis concerns the influence of arousal on rejection decisions, con-

trolling for offer size. In other words, what is the effect of offers on rejection rates that

are transmitted though changes in arousal, when the players are expecting a large power

shift? Following the dual process framework, we predict that the effect of low offers on

rejection rates that is transmitted through though greater physiological arousal will be

positive; that is, it will lower rejection rates. The effect of high offers will lead to higher

rejection rates, mediated by lower levels of physiological arousal.

16

Hypothesis 3: When there is a large power shift, the effect of offers on rejection rates

that is mediated by heightened physiological arousal will be positive. This mediation

effect will be absent in the low power shift condition.

3 Experimental Design

3.1 Lab Procedure

We conducted this study at the Harvard Decision Science Laboratory using 121 male

undergraduate students (agemean = 22) who signed up. Each session began with subjects

being hooked up to the physiological sensors described below. Then subjects read a set of

instructions that explained the basic rules of the bargaining game using neutral language.

A condition- and hypothesis-blind experimenter also gave the instructions verbally and

then answered any questions. After obtaining a baseline recording of the skin conductance,

the bargaining games began, described in Section 3.2.7 Each subject was randomly paired

with another subject and randomly assigned a position as described below in more detail.

Subjects then played the bargaining game sequentially. At each stage of the game a

unique signal was sent to the physiological recording device to indicate different outcomes

in the game, such as an offer being received, through parallel port communication. This

enables us to precisely match a given subject’s physiological response at a given time

to specific actions in the bargaining game. After playing 10 matches, subjects took a

short post-experiment questionnaire that included several policy questions and personality

inventories. Subjects were paid privately based on one randomly selected match. On

average, subjects earned $20 for approximately 50 minutes of time.

Before proceeding, we offer a disclaimer for those readers uncomfortable with the use

7Subjects watched a video (2m49s) featuring relaxing images of beaches and palm trees with calm

music in the background to measure the physiological responses at the baseline. This particular stimulus

and protocol has been used in previous research, and by the authors in Renshon et al. (2014).

17

of either lab experiments more generally or the specific use of samples of undergraduates.8

On the latter question, we note that while elite experiments are becoming somewhat

more common (Hafner-Burton et al., 2012, 2013; Renshon, 2015), they are logistically

implausible in many circumstances. Moreover, such experiments are only necessary and

desirable under a very specific set of circumstances. The primary rationale for such

experiments must be that leaders/elites are hypothesized to differ systematically from

convenience samples on dimensions that are theoretically relevant to the study at hand.

In the context of the current study, one would have to argue that, for example, elites would

be less likely to have emotional responses, which given some of our earlier discussion seems

unlikely. Even then, it may be unwise to use elite samples until convenience samples have

established the plausibility of a particular effect to begin with.

On the former question, concerns tend to cluster around the notion that–even if we

had access to subjects of theoretical interest–there is something artificial about the lab-

oratory which prevents us from generalizing to situations outside the lab. Here, we note

only that there is a long history of laboratory studies being replicated in diverse environ-

ments, using different samples, measures and contexts. This has occurred with aggression

(Anderson and Bushman, 1997), prospect theory (Camerer, 2004), donation experiments

(Benz and Meier, 2008), and more recently in political science as well (Ansolabehere et al.,

1999; Barabas and Jerit, 2010).9

Moreover, the common criticism of IR experiments that the stakes in the real world are

so high that experiments cannot mimic them rests on shaky foundations. In fact, empirical

work on this subject is relatively clear: stakes do not change the dynamic dramatically in

most instances, and to the extent they do, it is the inclusion of moderate stakes (compared

to no financial incentives) that make a difference, not marginally increasing stakes that are

already present in the experiment (see Camerer and Hogarth, 1999; Holt and Laury, 2001;

Hertwig and Ortmann, 2003).10 This is why our study was designed such that subjects’

8For a longer discussion of these issues, see Renshon (2015).9For an excellent discussion, see Levitt and List (2007).

10In fact, the relationship between incentives and performance does not appear to be entirely monotonic

when incentives are the extremely high, suggesting that ratcheting up the stakes is not necessarily an

18

decisions do have real (if small) economic consequences; subjects lose actual money if

they perform poorly, so there are strong incentives to pay attention and try to “win.”11

3.2 Experimental Game and Treatments

In our experiment subjects were anonymously paired with each other and randomly as-

signed to be in position A or B. After the second period each subject was randomly

matched with another subject and played the same 2 period game. Each period of the

game had the same basic structure. In period 1, player A proposes a division of a re-

source of size R = 10, (x1A, x1B = 10 − x1A). Here the subscripts represents the period

and position, so x1B is what player B would get from player A’s first period offer. Player

B decides whether or not to accept the offer. If they reject (i.e., choose a war lottery), the

entire resource is assigned by the computer to player A or B with probability p1 that A

wins the resource and 1− p1 B wins, where the subscript again represents period 1. Both

players also pay a cost cA, cB = 2. Following rejection in the first period, in the second

period the winner of the resource receives R = 10 points automatically. If the first period

offer is accepted, in the second period the same game is played with R = 10 points being

divided and both players stay in the same position (A or B).

The experiment had two treatment conditions that determined how the probability of

gaining the resources shifted from one period to the next. In BigShift p1 = .3 and p2 = .7.

In other words, player A starts out “weaker” in Period 1, but gains a significant amount

of power (i.e., higher probability of winning the costly lottery) such that in Period 2 the

power dynamics have reversed. In this situation, our game-theoretic model predicts that

player B is likely to reject offers in Period 1, since “taking their chances” in a Period 1

gamble is preferable to doing so in Period 2 once a major power shift has occurred. This

is illustrative of the commitment problem dynamics described earlier: player A has no

appreciate fix. See Ariely et al. (2009).11On the other hand, Kahneman and Tversky (1979) recommend large hypothetical gambles over

“contrived gambles for small stakes.” Notice that this solution would be even more unacceptable to those

political scientists worried about external validity than the inclusion of “only” small stakes. This may say

more about our almost religious beliefs concerns the appropriateness of various methods than anything

else.

19

way to credibly commit to not taking advantage of their increased power in the future

and player B thus has strong incentives to fight for the resource while their position is

advantageous.

In our second experimental condition, SmallShift, p1 = .49 and p2 = .51. In both

conditions, the power shifts in the same direction (player A becomes more powerful in the

second period), but in SmallShift the magnitude of the change is negligible and thus un-

likely to be associated with commitment problem dynamics. In this condition, our model

predicts fewer rejected offers and a higher likelihood of a “peaceful” bargaining resolution

as a result of the lack of a commitment problem. In particular, the model predicts that

any offer over 5.3 should always be accepted, whereas in the BigShift condition all offers

should be rejected (see appendix for additional details).

All aspects of the game are common knowledge. Subjects were paid based on one

randomly selected repetition of the experiment and received $1 for every 10 points earned.

3.3 Physiological Data Acquisition

Participants’ skin conductance levels (SCLs) were measured continuously throughout the

experiment. SCL is a reliable indicator of increased attention and arousal, and is asso-

ciated with greater insula activities (for reviews, see Christie, 1981; Sequeira and Roy,

1997). Skin conductance has also been used in similar contexts in past research to in-

vestigate the relationship between actors’ emotions (measured by physiological arousal)

and their decisions (Van’t Wout et al., 2006; Civai et al., 2010). Despite its important

advantages, one potential shortcoming of this measure of physiological arousal is that it

does not allow us to distinguish the valence of general feelings (i.e., positive or negative

feelings). However, given that one’s autonomic nervous system responses precede con-

scious awareness, and are difficult to control consciously (Gardner et al., 2000; Bechara

et al., 1997), we believe that the fluctuation (i.e., reactivity) in skin conductance should

provide valuable information about the extent to which intuitive vs. deliberate processes

are being utilized.

Skin conductance data for all participants was collected through the use of two dis-

posable Biopac (Santa Barbara, CA) electrodes (Model: EL507), which are filled with

20

Biopac Skin Conductance Electrode Isotonic Paste (specially formulated with 0.5% saline

in a neutral base). These electrodes were placed on the palms of the participant’s non-

dominant hand (the thenar and hypothenar eminences). A constant voltage of 0.5 V was

applied between the electrodes. SCL was then checked by research assistants to ensure

proper recordings, and following that participants watched a short video (2m49s) featur-

ing images of beaches and palm tress with calm music. SCL measurements of this time

period were used as “baseline” physiological arousal.

We followed the standard procedure of scoring the skin conductance data; raw mea-

sures were sampled at 1000 Hz, and amplified using a gain of 25µΩ and a low-pass filter

of 5Hz, using a BioNex mainframe and amplifier system, and BioLab 2.4 software (Mind-

ware Technologies, Gahanna, OH). Using Mindware’s software EDA module 3.0, research

assistants who were blind to both the study hypothesis and conditions calculated SCL (in

microsiemens). We then output the scored data into a time series. Finally, in order to

address potential individual differences in variability in skin conductance, our data were

transformed to deviations from the baseline condition (using the average SCLs while the

video was played) and standardized within each participant (see Ben-Shakhar, 1985; Bush

et al., 1993).

Our measure of SCL uses this standardized deviation from baseline score. To do this

our experimental design requires that we extract these standardized scores during the

period where decisions were made. We were able to do this because of the our procedure

of placing tags in the time series via parallel port communication (as discussed above).

Then, we took the average SCL deviation from the time after the offer was made, and

before responders make the decision to accept or reject the offer in the first round. This

average deviation from baseline during this particular phase of the experiment is our key

physiological variable.12

12Our physiological results are robust to using medians instead of means. Any deviations above 3 are

capped at 3 and below -3 is capped at -3, though our results hold not making this common restriction

which was rare in the data.

21

4 Results

We begin with simple descriptive statistics of the average first round offer in both condi-

tions. Figure 1 presents histograms of the amount offered to player B with vertical lines

indicating the average offers in the experimental conditions. Average offers in the BigShift

condition were slightly higher. Furthermore, the variation in offers was also much higher

in the BigShift condition. While the modal offer in both conditions was a 50/50 split,

there were many more offers above and below this point in the SmallShift condition. Next

we move to a discussion of our key hypotheses.13

SmallShift

Offer

Den

sity

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

BigShift

Offer

Den

sity

0 2 4 6 8 10

0.00

0.10

0.20

0.30

Figure 1: Histogram of first round offers by power shift condition.

4.1 Do Power Shifts Spur Commitment Problems?

Our results were consistent with Hypothesis 1, that offers are more likely to be rejected

in the BigShift condition. We estimated a probit regression model where the dependent

13Future versions of the paper could also investigate learning effects.

22

variable is whether or not the offer was rejected. The independent variables were the

size of the offer, an indicator for whether the experimental session used the BigShift or

SmallShift condition, and an interaction between the experimental condition and offer

size. Standard errors clustered at the individual level. Using the results of this model, we

then plot the predicted probability of an offer being rejected in Figure 2 using the Zelig

package in R.

Offers below 5 are almost always rejected in both the BigShift and SmallShift condi-

tions. Above an offer size of about 5, offers are more likely to be rejected when there is

a large power shift. That is, for more generous offers, individuals in both conditions are

more likely to accept the offers than less generous offers. However, for any of these more

generous offers they are more likely to be rejected in the BigShift condition.

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Offer

Pro

babi

lity

of R

ejec

tion

median

ci95

ci95

ci95

Big ShiftSmall Shift

Figure 2: Probability offer rejected as a function of offer size and whether power shiftlarge or small.

23

4.2 Do offers affect physiological arousal?

Next we investigate whether offer size affects arousal in the two experimental conditions.

To do this we estimated a simple linear regression model with our measure of arousal as the

dependent variable and offers as the independent variable.14 We found that higher offers

on average lead to lower levels of skin conductance but only in the BigShift condition,

t=-2.19, p<.05). In the SmallShift condition there was no significant relationship between

offers and arousal, t=-.3, n.s. To display the results, Figure 3 plots predicted arousal as

a function of offer size.

This finding suggests that responders in the BigShift condition were more physiolog-

ically reactive to low offers than to high offers, as we predicted. Lower offers made by

the rising power in the first round are perceived as more provocative, and may thus be

interpreted as a challenge, which might have activated more physiological arousal among

the responders. It should also be noted that the relationship between offer size and skin

conductance reactivity was more pronounced in the BigShift condition, as compared to

the SmallShift condition. This finding indicates that the typical outcomes of low offers –

aversive arousal – in the ultimatum game setting may not uniformly apply to our bargain-

ing setting. Due to the repeated nature of the bargaining, the anticipation of the power

shifts significantly moderates the effect of low offers on physiological arousal.

4.3 Do offers affect decisions through psychophysiological arousal?

Finally we turn to the role of physiological arousal in mediating the relationship between

offers and rejection decisions. The mediation effect is the change in the outcome while

holding the treatment condition constant but varying the values of the mediating variable.

Formally, the mediation effect under treatment condition t, δi(t) can be defined at the

individual level as:

δi(t) ≡ Yi(t,Mi(t))− Yi(t,Mi(t′)), (1)

14We also estimated generalized additive models that does not impose a linearity assumption. Results

were nearly identical to the linear model.

24

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Offer

Ave

rage

Ski

n C

ondu

ctan

ce S

core

median

ci90

ci90

ci90

Small Shift

Big Shift

Figure 3: Effect of offer sizes on skin conductance. 90% confidence intervals used forpresentational purposes and robust standard errors.

where Yi(t,Mi(t)) represents the value of the outcome variable under the treatment t. As

discussed elsewhere (Imai et al., 2011) inference about this requires the assumption of

sequential ignorability, where 1) there is no omitted variable that affects the treatment

and outcome and 2) there is no omitted variable that causes both the mediating variable

and outcome variable. In the current design, the offer is not randomized. But it is

implausible that rejection decisions by a different person (player B) could be influenced

by the same confounding variable that influences offer decisions (by Player A).15 The

second assumption is more difficult to deal with and can be approached either through

inclusion of pre-treatment controls, sensitivity analysis, or alternative designs (Imai et al.,

2013). We discuss each below.

We estimate a mediation model based on two parametric models. The first is the

model used in Section 4.2, which regresses arousal on offers. The second model uses

15All interactions were completely anonymous.

25

a probit regression where binary variable indicates whether the offer is rejected (1) or

rejected (0). We also permit an interaction between the treatment and mediator in the

outcome model, allowing for δi(t) 6= δi(t′). This could occur if the postulated arousal

process only occurs when offers are larger, rather than small. We estimate these models

separately for the two experimental conditions (BigShift and SmallShift).

Using the results from these models we estimate the mediation effects using the

methods described in Imai et al. (2010).16 With this method we must first define the

treatment contrast. In our setting this amounts to setting two treatment conditions,

t′, t, that correspond to two different offer levels. We focus on the contrast between

t′ = 5, t = 10. Thus, for example, in the second contrast δi(10) represents the change in

probability of rejection that occurs with an offer of the entire resource that is due to the

difference in physiological arousal (Yi(10,Mi(10)) − Yi(10,Mi(5))). A positive change in

probability is consistent with hypothesis 3.

Figures ?? and 4 plot the result for the BigShift (top) and SmallShift (bottom)

conditions. In each plot, the average causal mediation effect (ACME) for both treatment

conditions (dark line for t and dashed line for t′), direct effect, and total effect point

estimates and confidence intervals are reported. In both plots the mediation effect under

t is positive and statistically significant for the BigShift condition. The mediation effect

for an offer of 0 is not different for the BigShift condition, nor is either mediation effect

statistically different from 0 for the SmallShift condition. Consistent with hypothesis 1

and the previous results, the total effect of offers on rejection decisions is negative, large,

and statistically significant.

Controlling for offer size, higher levels of skin conductance lead to a lower probability

that the player chooses “war” (i.e., rejects offer). In the first stage model (regression of

offer on physiological arousal) the effect of the treatment is negative AND in the second

stage of the mediation model (rejection decision on offer and physiological arousal) the

effect of physiological arousal is negative. Thus the average causal mediation effect is

16Because a probit model is used, common approaches such as the product of coefficient method/Sobel

test are not applicable. We obtain substantively identical results if we use a linear model for the rejection

choice.

26

−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1

BigShift

TotalEffect

DirectEffect

ACME

−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1

SmallShift

TotalEffect

DirectEffect

ACME

Causal Effects

Figure 4: Mediation Effects for treatment change of 5 to 10. Top row BigShift treat-ment and bottom row SmallShift treatment, with 95% confidence intervals allowing forclustering at the individual level.

positive (the product of two negative effects is positive).17 The effect of increasing an

offer that is transmitted through changes in skin conductance increases the probability

of a rejected offer.

Two statistical considerations should be mentioned before proceeding. First, there

could be confounding pre-treatment variables that impact both our emotional measures

and outcome decision. Controlling for additional pre-treatment covariates of player B did

not change our results.18 Depending how an additional confounder impacts our emotional

measure and outcome, our results could be biased down or up. Unfortunately, the for-

mal sensitivity analysis proposed by Imai et al. (2010) that deals with omitted variables

17Again, to note the contrast with the UG, the first stage regressions would show a negative relationship

between offer size and arousal, whereas the second stage would show positive relationship between arousal

and rejection decisions.18We included a measure of right wing authoritarianism, generalized trust, and ideology.

27

effecting both the mediator and outcome is not possible here because our treatment vari-

able is continuous rather than binary.19 Second, we note that our measures of emotional

arousal will come with some degree of measurement error. What is the implication of

this for the current study? Given that the direct and indirect effects go in opposite direc-

tions, if anything we are likely to be under estimating the role of the emotional pathway

(VanderWeele et al., 2012).

Here, we found that higher levels of skin conductance do not necessarily predict more

rejection (war). Rather, higher levels of skin conductance actually predicted less rejection.

It should also be noted that this finding is robust even when offer size is controlled for.

On the face of it, this may perhaps seem puzzling; our intuitions typically lead us

to associate “emotional arousal” with aggression and conflict, but here the relationship

is reversed. Here, physiologically aroused subjects were less likely to choose war, and

more likely to accept player’s B’s first round offer. How do we reconcile this seeming

contradiction? The key is in the realization that if player B chooses war, they choose the

strategically optimal path. That higher levels of arousal are associated with the opposite

–accepting their adversary’s offer and taking their chances in a second round in which

their own power will be greatly diminished– suggests that the arousal is preventing sound

decision-making.

In sum, as we hypothesized, our data suggest that lower levels of physiological arousal

allowed participants to engage in more strategic thinking, while higher levels of arousal

inhibited this deliberate process. Despite the similarities of the ultimatum game and our

bargaining game, we argue that the two games are sufficiently different by design that

low offers did not necessarily led to homogeneous outcomes. In particular, the negative

effect of physiological arousal on rejection rates is indicative of the possibility that aversive

arousal impairs one’s ability to engage in strategic thinking, thus making it difficult for

the responders to choose the optimal strategy of rejection.

19Further, we note that while offers are not randomized within a condition, they are not a choice

variable of the person who is responding to the offer.

28

5 Follow-up Experiment: Shifting Power but No Shift-

ing Offers

In the previous section, we examined the effects of commitment problems by contrasting

two experimental conditions; one with a large shift, and one with a shift so small as to be

negligible. We found that the latter condition did not generate a commitment problem

by virtue of the fact that the shift in power was too small. This is one way to examine

the effects of a commitment problem, but it is by no means perfect. For example, the

BigShift condition might have primed fairness reference points (Kahneman, 1992). An

alternative manipulation of the commitment problem is to allow a large shift in power,

but prevent offers from changing in the first to second period (Quek, 2012). If a reduction

in concerns about shifting power occurs, then we should expect that the mediating role

of skin-conductance should also decrease.20

Figure 5 presents the results from a followup study that had the same large shift

in power, but did not permit offers to change from round 1 to round 2, using 36 new

subjects from the same subject pool. The results show that while increases in offers lead

to decreases in the probability an offer was rejected, the mediating role of our physiological

measure is now no longer statistically different from zero, with the point estimate quite

close to zero.

In other words, once we eliminated the commitment problem through the imposition

of institutional changes–here changing the rules of the game to prevent shifts in offers–the

affective mechanism linking offers to rejections disappears. Thus we have tried to “shut-

off” the commitment problem in two ways, with both having the same consequences for

our physiological measures. In Figure 6 we present the simulated impact of offers on our

skin conductance measure, and we see the same pattern as with the Small Shift condition

in Figure 3. By including this additional design we can be more confident that our results

20An alternative design would be to introduce communication where players could try to make verbal

commitments. This may or may not have the desired effect depending on whether cheap talk can be

persuasive (Tingley and Walter, 2011a).

29

relate to concerns about changes in offers that would occur in the future due to shifting

power.

−0.6 −0.4 −0.2 0.0

Big Shift no Offer Shift

TotalEffect

DirectEffect

ACME

Causal Effects

Figure 5: Mediation Effects for offer change of 5 to 10 using experimental condition thatallows for large shift in power, but no ability for offers to change from round 1 to round2, with 95% confidence intervals allowing for clustering at the individual level.

6 Discussion & Conclusion

Explanations for the failure of bargaining and the resulting conflict have centered heavily

in recent years on so-called “commitment problems” that arise from shifting bargaining

power. Because of the inherent difficulty in credibly committing oneself not to take

advantage of a rival in the future, bargaining under conditions of shifting power are likely

to result in violent conflict. This explanation is compelling, but makes no attempt to

connect to what individual, human, decision-makers might experience.

We posit a theory of “aversive arousal” that is activated under conditions of large

power shifts (but not, it should be noted, under stable conditions). While actors who

30

0 2 4 6 8 10

0.4

0.6

0.8

1.0

Offer

Ave

rage

Ski

n C

ondu

ctan

ce S

core

median

ci95

ci95

ci95

No Offer Change Allowed

Figure 6: Effect of offer sizes on skin conductance when large power shift and no oppor-tunity for changes in offer. 95% confidence intervals with robust standard errors.

face the prospect of substantially losing power should reject all offers, we show that offers

can trigger physiological reactions which may impair strategic reasoning that is part of

the deliberative, “System II,” process identified by psychologists. Nevertheless, we also

provide indirect evidence of System II thinking, in that for many offers rejection decisions

were more likely in the BigShift condition. This behavior is consistent with the predictions

of the rational choice model.

We have brought together a somewhat unusual combination of formal modeling to

derive hypotheses, psychological theories to suggest additional hypotheses, and experi-

mental methods and psychophysiological data to test those hypotheses. While this par-

ticular combination is not necessary in all cases, we hope that it serves as an example

of one promising way to test the micro-foundations of theories of conflict in a laboratory

setting. We also demonstrate how the role of physiological responses may differ depend-

ing on the type of game (e.g., previous studies look almost exclusively at the Ultimatum

31

game). A richer understanding of the relationship between emotion and decision-making

in different incentive environments would certainly be valuable (see Myers and Tingley,

tted; Lee et al., aper). Finally, unlike previous studies, we carefully design our experiment

in a way that lets us analyze the mediating role of physiological responses in a bargaining

setting using new statistical tools.

Of course, any successful experiment inevitably generates more questions than it

answers. In this case, we focus on deliberative versus intuitive thinking. However, a

large literature on emotions and bargaining suggests that specific emotions (e.g., anxiety,

anger) may be an important component of the process we describe in our study. Just as

importantly, one might start to add layers of complexity to the bargaining game we used

in order to more closely mimic important aspects of the international system, such as the

presence of international institutions that may under some conditions alleviate conflict

(e.g., by preventing shifts in offers from one period to the next). Finally, while we have

measured the effect of arousal generated in the game, future work could try and directly

manipulate this arousal. For example, if in the “Big Shift” condition we introduced a

greater time delay to making a decision, would we observe any differences as reflective

considerations kick in more?

Furthermore, there remain important questions about the applicability of such ex-

periments to the study of international relations. Our study uses a convenience sample.

We think the best way analytically to evaluate the impact of this is to “sign the bias.”

Recent work makes a good point that student subject pools and elite samples may differ

(Hafner-Burton et al., 2013; Renshon, 2015). Crucially, though, it is important to think

about whether any of the effects identified in the current paper would be magnified or

decreased were we to use an alternative sample. Such considerations are beyond the scope

of this paper, but our paper, we feel, provides an innovative platform for such a discus-

sion. Additionally, future studies might investigate important questions about selection

into crises. Perhaps those people that are more easily aroused also enter into zero sum

situations more readily because they are less able to recognize potential for joint gains?

Future experiments, and papers, designed with this in mind would speak to key themes

32

in the study of international negotiation (Odell and Tingley, 2013).

33

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43

APPENDICES

44

A Model of Commitment Problems

To see how power shifts can lead to conflict we provide a brief sketch of a simple two

period bargaining model.21 The basic intuition is that when one player expects to be

disadvantaged in the future, they have an incentive to start a conflict in order to forestall

the shift in bargaining power. There are two players, A and B. In each period there is a

resource with value 10. This resource may be divided between the players. The bargaining

protocol is as follows. In the first period player A makes a demand, x1A, to player B.

This leaves player B with 10− x1A. If the demand is accepted, then in the second period

there is another bargaining stage, where player A makes a demand x2A. If the first period

demand is rejected then both players play a war lottery, with probability p1 player A

wins. One player wins the resource for period 1, but both players pay costs cA = cB. The

winner of the lottery obtains the entire resource in period 2. If the resource is rejected in

the second period, both players pay the cost and play a war lottery, with probability p2

player A wins.

To analyze the complete information game we use backwards induction. We begin

with the second period decision by actor B. In Period 2 player B is indifferent between

demand x2A and lottery if (1 − p2) × 10 − cB = 10 − x2A. Thus if x2A = 10p2 + cB then

actor B is indifferent and by assumption accepts the demand. In period 2 player A’s

expected utility from the lottery is 10p2 − cA. Hence A will prefer to make a demand

x2A = 10p2 + cB if p2 + cB > p2− cA. This holds because cB = cA. They can’t make more

than this demand because then it will be rejected. So, the optimal demand in the second

period is x∗2A = 10p2 + cB. In the SmallShift condition this amounts to a demand of 7.1

and in the BigShift condition a demand of 9.

Now consider period 1. B’s utility from rejecting the lottery in period 1 is 10× (1−

p1)− cB + δ10× (1− p1), where δ represents the discount rate for the second period, or

the likelihood that the second period is played. We assume that δ = 1 for any numerical

calculations. Player B’s utility from accepting a demand x1A is equal to 10−x1A + δ(10×

(1− p2)− cB).

21This is simply a two period version of the model in Fearon (1995).

45

Thus player B will reject the demand x1A if

10× (1− p1)− cB + δ10× (1− p1) > 10− x1A + δ(10× (1− p2)− cB)

x1A > 10p1 + δ10p1 − δ10p2 + cB − δcB

Hence they will be indifferent if x1A = 10p1 + δ10p1 − δ10p2 + cB − δcB,

Now consider A’s expected utility in period 1. If they have the lottery rejected they get

10p1−cA+δ10p1. If they have some demand x1A accepted then they get x1A+δ(10p2+cB).

They will want their first period demand accepted if

x1A + δ(10p2 + cB) ≥ 10p1 − cA + δ10p1

x1A ≥ 10p1 + δ10p1 − δ10p2 − cA − δcB

Now note that the RHS of this is almost identical to what will make B indifferent,

except that it is slightly smaller (−cA instead of cB).

Hence A will make demand x∗1A = 10p1 + δ10p1− δ10p2 + cB − δcB. In the SmallShift

condition this will be a demand of 4.7. Hence offers over 5.3 in the first round will be

accepted.

The key question is when the first period demand will be rejected. This will occur

when x∗1A is less than 0. That is, when player A can not offer (demand little) enough to

make player B accept the demand in light of what they expect to get in period 2. This

holds when we have 0 > 10p1 + δ10p1− δ10p2 + cB − δcB. Assuming δ = 1 this reduces to

p2 − 2p1 > 0. Thus as p2 gets larger and/or p1 gets smaller, this condition is more likely

to hold.

In the experiment that follows, our BigShift condition has p1 = .3 and p2 = .7 and

our SmallShift condition has p1 = .49 and p2 = .51. In the BigShift condition p2−2p1 > 0

holds and so we expect preventive war, but in the SmallShift condition this condition does

not hold. Demands less than 4.7 should be accepted.

46