WHY CAN’T ECONOMISTS SEE

THE GOOD IN EVERYONE? A Survey Paper On Fairness and Altruism

Faisal Haider fh586@nyu.edu

Abstract A survey paper discussing research on the phenomena of fairness and altruism and how current

research into them may aid theoretical predictions

Fairness and Altruism

All disciplines have certain assumptions which are essential to analysis and study. For

economics, the characteristics of an individual agents is incredibly important to understanding how

and why agents act and react in certain situations. In subfields such as game theory, the validity

and strength of these assumptions become incredibly important. Rationality is one of the key

assumptions of neoclassical economics. A rational agent is an agent that has clear preferences,

models uncertainty via expected values of variables or functions of variables, and always chooses

to perform the action with the optimal expected outcome for itself among all feasible actions1. As

the primary assumption when dealing with individual agents, the validity of each and every one of

these characteristics for a rational agent affects how close theory comes to reality. In the world of

experimental economics and game theory, these rational agents are the crux of research and theory;

in order to measure these subjects and their optimal actions, economists resort to utility theory,

which related to understanding the “rationality” of economic agents. Flaws with the basic tenets

of utility theory may lead to deviations from theoretical predictions and better explain experimental

data once solved. If true, the critical analysis of each of the defined characteristics of a rational

agents could be very important in understanding why experiments result in outcomes that do not

converge or are antithetical to theoretical predictions. In the following survey paper, I will focus

on experiments regarding a rational agent’s choice of actions that yield the optimal expected

outcome for itself among all feasible actions. I will contrast this assumption with experimental

papers that discuss the phenomena of fairness and altruism in game theoretic settings in an effort

to better understand the relationship between rationality, utility, fairness and altruism, in the hope

of understanding if the definitions of each are sufficient in characterizing economic agents.

1 Wikipedia, “Rational Agent”. Accessed 11-30-15. https://en.wikipedia.org/wiki/Rational_agent#Economics.

Altruism is the principle or practice of concern for the welfare of others. In economics,

pure or simple altruism implies that agents may not only care about their own wellbeing, but also

the wellbeing of others2. Although taking such actions may not be personally optimal, the altruistic

agent may cause the total payoffs to be higher. Yet, pure altruism is as extreme as pure rationality

(whether these two are true dichotomies will be discussed later); from circumstantial evidence, it

does not seem that most people could only be classified as altruistic or rational. Hence, we must

consider the concept of fairness in economics; can and do the actions of one agent influence the

actions of a non-empty subset of agents in the population due to either an internal or environmental

stimulus? If true, this would explain certain deviations from game-theoretic predictions. Cooper,

Dejong, et al discuss the phenomenon of altruism in the Prisoner’s Dilemma, where, for a subset

of players, cooperate is not a dominated strategy3. In fact, when the authors ran a finitely repeated

game versus one-shot games, the frequency of cooperative play was higher in instances where

reputation could be built (i.e. when two individuals played together for a certain amount of

periods). Yet, the frequency of cooperative play for both cases seems to converge to 0, which is

the game-theoretic prediction for all periods of play of the Prisoner Dilemma game. Could this

mean that altruism is a mistake on the part of the subjects? As Rabin discusses in his paper,

psychological evidence indicates that most altruistic behavior is complex.

In his examinatory paper about the importance of fairness in economics, Rabin comments that

people do not seek uniformly to help other people; rather, “the same people who are altruistic to

other altruistic people are also motivated to hurt those who hurt them”4. The notion of an economic

quid pro quo allows for a definition of fairness equilibria: neither a refinement nor a replacement

2 Matthew Rabin, “Incorporating Fairness into Game Theory and Economics,” The American Economic Review (Dec 1993), pp 1281. 3 Cooper, Dejong, et al, “Cooperation without Reputation: Experimental Evidence from Prisoner’s Dilemma Games,” Games and Economic

Behavior (12), pp 188. 4 Rabin, “Incorporating Fairness”,pp 1281.

of the Nash equilibrium, the fairness equilibrium includes individual understandings and beliefs

about fairness in addition to the utility from payoffs. He defines mutual max outcomes as a set of

actions such that, given the other person’s behavior, each person maximizes the other’s material

payoffs: mutual min outcomes is similarly defined. Since the magnitude of payoffs is important in

evaluating fairness, Rabin further defines the fairness equilibrium: (i) Any Nash equilibrium that

is either a mutual-max outcome or mutual-min outcome is also a fairness equilibrium: (ii) if

material payoffs are small, then, roughly, an outcome is a fairness equilibrium if and only if it is a

mutual-max or mutual-min outcome: (iii) If material payoffs are large, then, roughly, and outcome

is a fairness equilibrium if and only if it is a Nash equilibrium5. How agents view the payoffs is

important in understanding what action they choose and why they may deviate from game-

theoretic predictions.

Rabin then applies the fairness equilibrium to several types of games, including the

Prisoner’s Dilemma and the Ultimatum Game. His explanation of the Prisoner’s Dilemma from

this perspective does explain why PD experiments (especially the experiment done by Cooper,

Dejong, et al) lead to non-zero levels of cooperation; initially, the population may be attempting

achieve the mutual max outcome, but as players realize that a certain proportion is attempting to

maximize its own utility rather than the overall utility, other players begin to play actions that yield

the mutual min outcome. On the other hand, in the Ultimatum Game, Rabin states that “the result

of pure self-interest is clear: proposers will never offer more than a penny, and deciders should

accept any offer of at least a penny… [yet] data shows that, even in one-shot settings, deciders are

willing to punish unfair offers by rejecting them, and proposers tend to make fair offers”6. Thus,

5 Rabin, “Incorporating Fairness,” 1282. 6 Rabin, “Incorporating Fairness,” 1284.

for at least the subjects involved in these experiments, the concept of fairness (and more

specifically, the violation of it) caused a disutility that outweighed the benefit of accepting the

offer. Returning to a question previously posed, it would seem that at least fairness is not a mistake

on the part of the subjects and/or agents; rather than being concerned only for his/her own payoffs,

it would seem that there is a (conscious) willingness to forgo individual utility for a chance at

greater communal utility. In situations where the results of pure self-interest motivate non-

cooperate behavior to the extent that it cannot be rectified by communal action (like in the PD),

concepts of fairness may affect initial divergence from the game-theoretic prediction, but the

results seem to converge to the prediction eventually. Though Rabin does not explicitly discuss it,

special attention should be paid on whether the probabilities of the unfair outcomes being rectified

affects fairness evaluations; if there is a low probability that rejecting the offer will help others, or

even oneself, would players still reject unfair offers? How is this related to learning mechanisms?

Is fairness important in such decisions because it is a barometer of utility? Ultimately, Rabin is

interested in whether fairness can be coerced in certain situations. Could a player do something

that will compel another player to regard him positively and thus the two could work to achieve a

mutually beneficial outcome? This is exactly the question that is raised in a paper by Cox,

Friedman, and Sadiraj (CFS) about revealed altruism.

Much like Rabin’s paper, CFS analyzes and characterizes the beliefs of players in various

game-theoretic settings in order to understand how beliefs about others affect outcomes. Here, the

authors distinguish between conditional altruism – positive and negative reciprocity – from

unconditional altruism (also known as pure or simple altruism). Conditional altruism is related to

fairness equilibria in Rabin’s paper: “More generous choices by one player induce more altruistic

preferences in a second player; by the same token, less generous choices by one induce less

altruistic preferences in the other”7. In a sense, they go further than Rabin does by characterizing

individuals rather than just understanding differences in equilibria when fairness is introduced.

The authors argue that a Second Mover (SM) will respond more strongly to generous (or

ungenerous) choices that overturn the status quo than to those that uphold it or that involves no

real choice by the first mover (FM)8. Thus, the more income that the FM gives up or takes in

games, the stronger the reaction from the SM. Choosing an action that is not the “self-optimal”

action for the FM may actually help him. To prove this, the authors look at experimental data from

other studies on the Dictator Game, Carrot and/or Stick game, and the Stackelberg Duopoly. They

do not find significant results from the Dictator Game, but they do find that in the Carrot and/or

Stick game, the amount that the FM sends to the SM has a significantly positive impact on the SM

response in all games and regimes9. The only caveat is that this evidence must be taken with a

grain of salt, as the authors used a previous experiment’s data and only included the last five rounds

(they do not mention how many rounds were performed, which leads to issues with agreeing with

the validity of their observations).

The most interesting part of this paper, though, is the modification of the Stackelberg

Duopoly game into the Stackelburg mini-game, where the Leader (aka the FM) has a binary choice,

with one being the “more generous” choice. In the experiment the authors conducted, they wanted

to see whether intentions did affect the SM’s reaction. Although the quantity, qL = 9, is actually

the most altruistic action in this game (i.e it gives both players the highest payoff when the entire

range is available for consideration), the SM responded negatively when it was the less generous

choice (i.e the other quantity was considered better by the SM). The authors conclude that, contrary

7 Cox, Friendman, and Sadiraj, “Revealed Altruism,” Econometrica, Vol 76, No 1 (Jan 2008), 40. 8 Cox, “Revealed Altruism,” 40. 9 Cox, “Revealed Altruism,” 48.

to standard revealed preference theory, their model predicts that the SM’s response depends in a

specific way on the alternatives not chosen by the leader10. Hence, not only do beliefs matter when

acting, intentions do.

Intentions are exactly what are discussed in the next paper by Falk, Fehr, and Fischbacher.

The authors conjectured that the presence of fair-minded people is likely to have important

economic effects. But do fair-minded people respond to fair or unfair intentions, or do they respond

solely to fair or unfair outcomes? The authors attempted to test whether two premises affect

responses: what if the first mover’s choice set actually allows the choice between a fair and unfair

action? Does it matter if the first-mover’s choice is under the first mover’s full control?

To test, they re-enacted the moonlighting game with 112 subjects, 66 in the Intention

treatment and 46 in the non-Intention treatment. No economics students were included and all

participants were from the University of Zurich or the Swiss Federal Institute of Technology in

Zurich. The moonlighting game is a two player sequential move game that consists of two stages

where each player is endowed with 12 points. A chooses action a from the set, {-6, -5, …. 5, 6},

in first stage. If A chooses a ≥ 0, he gives player B a tokens while if he chooses a < 0, he takes a

tokens away from B. if a ≥ 0, the experimenter triples a when giving it B. After player B observes

a, she can choose an action b from the set, {-6, -5,…, 5, 6}, at the second stage, where b ≥ 0 is a

reward and b < 0 is a sanction. A reward transfers b points from B to A. Sanctioning costs B exactly

b but reduces A’s income by 3b. Hence, this allows for both positively and negatively reciprocal

behavior. A’s action signals fairness intentions if: A’s choice set allows the choice between

saliently fair and saliently unfair decisions, and if A’s choice is under his full control. There were

10 Cox, “Revealed Altruism,” 51.

two treatments; Intention Treatment (I-Treatment) and Non-Intention Treatment (NI). The I

treatment allowed player A to make decisions about his intentions; if a was high, it was intentional

kindness, but if a was low, it was intentional unkindness. On the other hand, players in the NI

treatment had two 10 sided die, where the rolls would correspond to a realized number between 0

and 99, with a probability of certain moves for A determined beforehand. Each player B was told

this in advance, thus informing them that it was random. The probability distribution was co-opted

from the original moonlighting experiment by Abbink et al (2000)11.

If it is common knowledge that all players are selfish and rational, by backwards induction,

B will always choose b = 0 in both treatments since any other choice would be costly and thus A

will choose a = -6 to maximize his/her own profit. A would not have a choice in the NI treatment

and thus would just play whatever random strategy is chosen. The actual results were drastically

different from the backward induction prediction; in the I treatment, there were no player B’s that

chose to play b = 0 for all the moves of player A. There was a general positive relationship between

A’s choice of a and B’s choice of b, indicating B’s willingness to “match” A’s (un)kindness. In

fact, when the authors looked at individual behavior, they found very interesting results; 21% of

subjects in the I treatment chose to reward but not punish, while 15% chose to punish but not

reward, indicating that the population was diverse. In the NI treatment, about 30% of player B’s

chose to play the backwards induction move of b = 0 for all (random) a12; the intention behind this

action did not coincide with the “selfish and rational” rationale and instead was influenced by the

fact that A had no control over his/her actions. Even for the subjects that did not choose b = 0 for

all (random) a, the positive relationship between a and b was much weaker than in the I treatment,

11 Falk, Fehr and Fischbacher, “Testing Theories of Fairness – Intentions matter,” Games and Economic Behavior 62 (2008), 293. 12 Falk, “Testing Theories of Fairness”, 299

indicating that intentions do shape actions; if an individual is forced to perform an action (or at

least if it seems so), the repercussions are less than if they had full control. This is important in

affecting standard utility theory; rather than just being concerned with material payoffs, there are

other considerations for players and agents.

Introducing an audience further diverges experimental results with theoretical results while

also affording interesting observations. In their paper about social image, Andreoni and Bernheim

note that “even when one party has all the bargaining power (the dictator game), typically 20 to 30

percent of subjects voluntarily cede half of a fixed payoff to another individual”13. To test this,

they set up a two player dictator game, where the dictator (D) splits a prize, x, with a receiver (R).

With probability 1 – p, D chooses the transfer, and with probability p, nature sets it equal to some

fixed value, x0; then the game ends. By adding the nature parameter, the authors can switch

between a dictator game (p = 0) to an extended dictator game. The parameters, p and x0, are

common knowledge but R cannot observe whether nature intervened. Potential dictators are

differentiated by a parameter t, which indicates the importance placed on fairness; its value is D’s

private information. D cares about his own prize, c, and his social image, m, as perceived by some

audience A, which includes R (and possibly others, such as the experimenter). D’s utility also

depends on the most fair alternative, xF (= 0.5*20 = 10 for this experiment since everyone is equal).

In essence, the inclusion of an audience creates the ability for D to signal to the audience whether

he/she cares about fairness. Thus, there is a pooling equilibrium at 0.5*x (= xF), where the pooling

equilibrium is a point where the audience cannot determine the D’s type, thus preventing his/her

social image (m) from decreasing if the D does not care about fairness. In this experiment, the pair

must divide $20 so the pooling equilibrium is at $10 and at x0 (when p > 0 and x0 is close to 0). To

13 Andreoni, Berheim, “Social Image and the 50-50 Norm,” Econometrica, 1607.

test this, the authors set x0 at either 0 (called condition 0) or 1 (condition 1) and allowed p to take

values of 0, 0.25, 0.5, and 0.75.

For condition 0, at p = 0, there is a spike at x=10, where 57% of pairs divided the prize

equally. Still, 30% chose x = 0. As p increases, the spike at x=10 shrinks and the spike at x=0

grows. There is a statistically significant increase in pooling at x = x0 when p rises from 0 to 0.25

and from 0.25 to 0.5 but not when p rises from 0.5 to 0.75. There is a statistically significant decline

in pooling at x = 10 when p rises from 0 to 0.25 and from 0.25 to 0.5, but not when p rises from

0.5 to 0.75. For condition 1, 69 percent of dictators divided the prize equally, while 17 per cent

kept the entire prize (x = 0) and only 3 percent (one subject) chose x = 1. As they increased p, the

spike at x = 10 once again shrinks. In this case, however, a new spike emerges at x = 1. As p

increases to 0.75, the fraction of dictators choosing x = 1 rises steadily from 3 percent to 48 percent,

while the fraction choosing x = 10 falls steadily from 69 percent to 34 percent. Notably, the fraction

choosing x = 0 falls in this case from 17 percent to 10 percent14.

These results indicate that fairness may be a barometer for selfishness and/or altruism.

Additionally, it would seem that in instances of complete (or nearing complete) information,

selfish/ self-optimal outcomes are less desirable in situations where reputation matters. This is

interesting because neo-classical economists believe in free-market, which is supposed to be a

market in which there is complete information; hence Smith’s argument that one could actually

help the entire population by being selfish may be true. Yet, we see that an increase in information

asymmetry actually hurts the fairness in the system. Thus, we see that people are fair and would

like others to see them as fair, yet are not afraid to take advantage of information asymmetries.

14 Andreoni, Bernheim, “Social Image,” 1622-1624.

From the past two papers, it would seem that information symmetry, or rather complete

information, is very important to harboring fairness and altruism. The lack of information allows

predation to occur. An interesting dimension to consider would be to determine what the minimum

fair price and whether it affects the statistical significance of changing the probability that nature

will intervene. Determining this would probably help us to understand whether the D is unfair

because he is selfish or because he does not believe that the accepted fair division is what it should

be.

The final paper to be discussed is about the “ratchet effect” in firms, as discussed in the

paper by Cooper, Kagel, et al. The ratchet effect occurs when a central planner (CP) differentiates

between high-productivity (HP) and low-productivity (LP) firms. Since a central planner will

continuously give the HP more work, it will need to exert more effort if it signals to the CP that it

is a HP. Thus, the HP would rather pretend to be a LP and attempt to find the pooling equilibrium

so that it won’t signal that it is, in fact, a HP. In the specific scenario for the paper, both HP and

LP had to choose between effort levels of 1 to 7 while the CP would assign either a tough or easy

contract to one or both firm(s). The pooling equilibrium for the game is an effort level of 2 for

both HP and LP. The study looks at how age and experience affect the rate at which strategic play

is achieved. Yet, I would like to bring some parallels to the other studies and understand why the

HP would not like to do what is optimal for all of the parties (i.e. differentiate and signal that it is

a HP). In essence, the issue boils down to information asymmetry and a mismatch of incentive.

The CP and the firms do not have matched incentives, that is, the CP would like the highest level

of output and the firms would like the minimum amount of effort. If bargaining were involved, it

would be interesting to see how it would affect the situation, since I had mentioned previously that

fairness possibly occurred only when there were equalizing conditions, either because of the

situation or the environment. If there were bargaining such that the firms and CP had equal, or near

equal, power, it could and would most likely be possible to sustain collusion where the HP would

work at effort level 5 (the highest output for the firm) and LP would work at 2 (its highest output).

Altruism and fairness can be seen as a violation of standard utility theory, since it implies

that agents do not only care about outcomes. If altruism is a signal that is correctly interpreted (and

thus included in their decision making) by other rational agents in the environment, altruism may

lead to a higher long term payoff at the expense of lower payoff in the short term, which is

tempered by intentions. But if the selfishness of economic agents is removed from the equation,

or at least treated as a dummy variable that may or may not be present due to the situation, then it

may be possible to make better predictions. Personally, I find the game theoretic assumptions too

strict, which leads to convergence with observed values only in extreme cases (where pay or

punishment is high). Although economics strives to be as analytical and objective as possible,

some humanity must be preserved, considering the focus of the subject.

Bibliography

Andreoni, James, and Bernheim, Douglas B., “Social Image and the 50-50 Norm: A Theoretical

and Experimental Analysis of Audience Effects,” Econometrica, Voll 77, No 5 (Sept 2009),

1607-1636.

Cooper, Dejong, et al., “Cooperation without Reputation: Experimental Evidence from Prisoner’s

Dilemma Games,” Games and Economic Behavior 12 (1996): 187-218.

Cooper, Kagel, Lo, and Gu, “Gaming Against Managers in Incentive Systems: Experimental

Results with Chinese Students and Chinese Managers,” The American Economic Review,

Vol. 89, No 4 (Sep 1999), 781-804.

Cox, Friendman, and Sadiraj, “Revealed Altruism,” Econometrica, Vol 76, No 1 (Jan 2008),

31-69.

Falk, Fehr, and Fischbacher, “Testing Theories of fairness – Intentions matter,” Games and

Economic Behavior 62 (2008), 287-303.

Rabin, Matthew, “Incorporating Fairness into Game Theory and Economics,” The American

Economic Review (Dec 1993), 1281-1302.

Wikipedia, “Rational Agent”, Accessed 11-30-15.

https://en.wikipedia.org/wiki/Rational_agent#Economics.