Bargaining and Social Preferencesuctpsc0/Teaching/ECON3020/SocPref.pdf · In this lecture we...

Bargaining and Social Preferences

Syngjoo Choi

Spring, 2010

Experimental Econometrics (ECON3020) Soc. Pref. Spring, 2010 1 / 30

Bargaining

Bilateral bargaining is pervasive in both markets and non-marketinteractions (such as legal and political disputes), and in bothdeveloping and developed economies.

Experimental research has conducted studies on both unstructructedbargaining and structured bargaining.

In the structured bargaining setting, the timing and sequence ofdecisions are limited in a way that permits the calculation of Nashequilibria and highlights the con�icts of interests.

In this lecture we overview some important experiments and their�ndings.


Social Preferences

Social preferences refer to the concern that people have for eachother�s well-being, such as altruism, fairness and reciprocity.

The classical approach in economics assumes that an individual isself-interest. Or it suspects that any social preference other thanself-interest may be fragile.

G. Stigler (1981), "When self-interest and ethical values with wideverbal allegiance are in con�ict, much of the time, most the time infact, self-interest theory ... will win."

We will start with a two-player game, known as ultimatum bargaining,that highlights an extreme con�ict between sel�sh, strategic behaviorand notions of fairness.


Ultimatum Bargaining Game

There are two players (the proposer and the responder) who want todivide £ 100 between themselves.

The proposer makes a take-it-or-leave o¤er that must be accepted orrejected by the responder.

If the responder accepts the o¤er, each would receive as speci�ed inthe o¤er. Otherwise, both would have nothing.


Equilibria in Ultimatum Bargaining Game

Assume that both players are sel�sh and rational.

(Nash Equilibria): the proposer makes an o¤er (x , 100� x) and theresponder accepts any o¤er which gives him at least 100� x (This isa NE for any x 2 [0, 100]).Nash equilibrium is subject to the issue of whether the responder�sstrategy is �credible�:

Suppose that the responder�s strategy is rejecting any o¤er which giveshim less than $50.When the responder turns out to face the proposer�s o¤er giving him$45, is it �reasonable� for him to reject this?

This issue of credibility can be further dealth with the notion ofSubgame Perfect Nash Equilibrium (SPNE).

A SPNE is a NE whose strategies are a NE in each subgame.The unique SPNE is the proposer makes an o¤er (100� ε, ε) and theresponder accepts any o¤er ε (or ε = 0).




(Nash Equilibria): the proposer makes an o¤er (x , 100� x) and theresponder accepts any o¤er which gives him at least 100� x (This isa NE for any x 2 [0, 100]).

Nash equilibrium is subject to the issue of whether the responder�sstrategy is �credible�:








Suppose that the responder�s strategy is rejecting any o¤er which giveshim less than $50.

When the responder turns out to face the proposer�s o¤er giving him$45, is it �reasonable� for him to reject this?









A SPNE is a NE whose strategies are a NE in each subgame.

The unique SPNE is the proposer makes an o¤er (100� ε, ε) and theresponder accepts any o¤er ε (or ε = 0).


Ultimatum Bargaining Game in the Lab

A typical �nding in many lab experiments is shown below (Ho¤man,McCabe, and Smith (1996)): responders reject o¤er less than 20% ofthe total money around half of the time and, anticipating this,proposers often o¤er between 30% and 50%.


Cross-Culture Bargaining Experiments

Several anthropologists (see Jean Ensminger (2002)) conducted thesame games in many di¤erent areas:


Market Integration and Fairness


Distinguishing from Altruistic Preferences to StrategicConsiderations

In the ultimatum bargaining game, the generous o¤ers by theproposer could come out because he is fair-minded or because he isafraid of having low o¤ers rejected (or both).

These two explanations can be easily separated in a Dictator Game,which removes the responder�s ability to reject o¤ers.

If the proposer o¤er positive amounts in the dictator game, he is notmaximizing only his own payo¤s but cares about the other�s payo¤.

A modi�ed version of dictator game can reveal an individual�spreference regarding others, through choices.


A Modi�ed Dictator Game

In the original dictator game one subject is asked to divide $Mbetween himself and another subject such that πo + πs = M.

Andreoni and Miller (2002), Fisman, Kariv and Markovitz (2007)provided a modi�ed version of the dictator game in which subjects aregiven a menu of choices with di¤erent endowments and prices forpayo¤s, such that πo + pπs = M.

oπ

mp so =+ ππ

sπ


A Modi�ed Dictator Game

In the original dictator game one subject is asked to divide $Mbetween himself and another subject such that πo + πs = M.Andreoni and Miller (2002), Fisman, Kariv and Markovitz (2007)provided a modi�ed version of the dictator game in which subjects aregiven a menu of choices with di¤erent endowments and prices forpayo¤s, such that πo + pπs = M.

oπ

mp so =+ ππ

sπ


Sel�sh Preference

The utility representation of sel�sh preference can be written:

u (πs ,πo ) = πs .


Sel�sh Preference

The utility representation of sel�sh preference can be written:

u (πs ,πo ) = πs .

FKM found around 26% of their subjects showing sel�sh preference.


Utilitarian Preference (or Perfect Substitute Preference)

The utility function for utilitarian or perfect substitute preference is

u (πs ,πo ) = πs + πo .


Utilitarian Preference (or Perfect Substitute Preference)

The utility function for utilitarian or perfect substitute preference is

u (πs ,πo ) = πs + πo .

FKM found around 3% of their subjects showing this preference


Rawlesian (or Leontief) Preference

The Rawlesian or Leontief utility function is

u (πs ,πo ) = min fπs ,πog .


Rawlesian (or Leontief) Preference

The Rawlesian or Leontief utility function is

u (πs ,πo ) = min fπs ,πog .

FKM found around 3% of their subjects showing this preference


Responders�Behavior in Ultimatum Bargaining Games

The most puzzling behavior is that of responders: why do so manyresponders reveal a preference for allocations that give both playersless consumption?

A common answer is that they must care about the relativeallocations of the players, described as fairness, spite, or reciprocity.

Therefore, it is natural to investigate what responders�preferenceslook like.

However, the ultimatum game, by its all-or-nothing nature, makes itdi¢ cult to discern what kind of preferences may be generatingchoices.


A Convex Ultimatum Game

Suppose there is a �xed amonut of money, M.

The proposer �rst speci�es the proportion of each money, a 2 [0, 1],that will go to the responder.

Then the responder determines how much money to to divide,m 2 [0,M ].The payo¤ functions for the proposer, πp , and the responder, πr , are

πp = (1� a)�m,πr = a�m.

If m can be only either 0 or M, then the game reverts to the standardultimatum game.


A Graphical Representation of Convex Ultimatum Game

Final outcome

pπ

rπ

Proposer’s Offer


What Can We Learn from Convex Ultimatum Game?

Suppose both players are self-interest. The standard game theorypredicts the same result in the convex game as in the standardultimatum game.

A responder will never shrink any o¤er. The proposer knows this andwill make the most sel�sh o¤er possible.

Suppose that responder�s preference is nonmonotonic in both playerspayo¤s (caring about relative allocations between them or inequalityaverse) but the indi¤erence curves are linear. Then both gamespredicts the same result.

Both players will settle in a particular relative payo¤. The responderwill nver shrink the allocation proposed by the proposer in equilibrium.

There will be a di¤erence between the two games when responder�spreference is nonmonotonic in both players payo¤s and indi¤erencecurves are nonlinear.


A Graphical Illustration


Best Reply Functions: Ultimatum vs. Convex Games


Experimental Design (Andreoni et.al (AER 03))


Inequality-Averse Preferences (Andreoni et. al)


Classroom Experiment

Go to Charles Holt�s Veconlab website,http://veconlab.econ.virginia.edu/login.htm.

Session name: ___


Trust Game I

The game you just participated in is called the Trust Game whoseexperiment was �rst reported by Berg, Dickhaut, and McCabe (1995).

There are two players (the �rst mover and the second mover). The�rst mover who is given $10 decides how much (if any) of this moneyto pass to the second mover, say $X .

Money that is passed is multiplied by a factor 3 (or 6), $3X , before itis given to the second mover, who in turn decides how much to returnto the �rst person, $Y .

The payo¤ for the �rst mover is ($10� $X ) + $Y . The payo¤ forthe second mover is $3X � $Y .


Trust Game II

If both individuals are sel�sh and rational, then the SubgamePerfection argument leads to the conclusion that the �rst moverpasses nothing to the second mover (why?).

The action of passing money initially would signal that the �rst mover�trusts� the second mover to reciprocate his behavior.

Trust is risky because the �rst mover will regret having entrusted if hedoes not get much back.

In this sense, the amount passed to the second mover measures trust.The amount returned measures trustworthiness.


Experimental Findings

Berg, Dickhaut, and McCabe ran this experiment with 32 pairs ofparticipants in a single round interaction.


Discussion

Since the act of passing money in the trust game is risky, it might bethat people who pass large amounts might simply be more willing totake a risk. (Karlin, 2005)

How can one design an experiment if he/she wants to isolate puretrust from risk-taking behavior?


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