Upload
faisal-haider
View
19
Download
0
Embed Size (px)
Citation preview
WHY CAN’T ECONOMISTS SEE
THE GOOD IN EVERYONE? A Survey Paper On Fairness and Altruism
Faisal Haider [email protected]
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.