Behavioral game theory

Behavioral game theory tries to determine how people actually behave in strategic situations by using experimental settings. To understand the gist of the evidence, we need some terminology:

· Homo Sociologicus: follows prevailing norms without regard to self-interest; a human is a tabula rasa on which society writes its mores. It is associated to the view that there is no such thing as human nature and the idea that, behaviorally speaking, we are our own makers.

· Homo Economicus: is self-regarding in that he always maximizes his own payoff without concern for others; in other words, he is selfish. Homo economicus became important in the xvii century; it underlies much economic theory and much social contract theory.

· Homo Reciprocans: cooperates conditionally on others’ cooperation and punishes shirkers even at a net cost to himself; in other words, he adopts strong reciprocity

Two different sense of selfishness must be distinguished

1. Game-theoretical selfishness: acting in such a way as to maximize one’s payoff, independently of motive. Being self-regarding is another term for being game-theoretically selfish.

2. Intentional selfishness: intending to maximize one’s own payoff.

Obviously, an animal may adopt a strategy which satisfies (1) without being able to form any intentions at all. Hence, what counts as payoff depends on the nature of the game and not on the intentions, if any, of the agent. For example, in an evolutionary game, the payoff is reproductive fitness, and therefore one may be a complete altruist (one who maximizes the payoff of others) even if the reason for doing it is the ‘selfish’ reason of avoiding guilt. Consequently, issues surrounding Psychological Egoism are irrelevant to egoism or altruism or any mix of the two in the game theoretical sense.

Rational Egoism, the view that only self-regarding actions and intentions are rational, so that the only reason (vs. motive) to do something is if it maximizes one’s payoffs, typically understood as the satisfaction of self-regarding desires.

In effect, the justification of any action must be reducible to self-interest. For example, Paley justifies one’s moral actions by arguing that they are beneficial to one. However, this view is also controversial because situations like the Prisoners Dilemma show that being self-regarding need not lead to optimal equilibriums. To what extent humans actually approach rational egoism is hard to tell; however, it seems clear that at times they adopt some form of bounded rationality in which psychological predispositions, computational deficiencies, and time constraints lead to simplifying assumptions and heuristic procedures that are satisficers, resulting in satisfactory rather than optimal solutions.

So, what assumptions about players should one make when constructing a model of human strategic behavior?

It turns out that when modeling market processes (e.g., supply and demand situations) with clearly defined contracts and the shared belief that individuals behave selfishly, the assumption that agents are self-regarding, albeit with bounded rationality, leads to correct predictions. However, in social dilemmas (all gain if most cooperate while each has a personal incentive to defect) modeling with self-regarding players is not successful: homo economicus does not work well. One might then turn to homo sociologicus, but this does not work well either: often individuals do not follow social norms if it is advantageous to them and can operate anonymously (This is true also of societies which value sociality very highly. For example, when acting anonymously, Japanese have lower levels of cooperation than Americans). Does homo reciprocans work?

First, it may be helpful to look at some experimental evidence. Consider the following three games:

· The Ultimatum game: under anonymity, A and B are shown, say, $10. A is told to offer any amount out of the $10 to B. B may accept or refuse. If B accepts, then the money is distributed accordingly. If B refuses, then nobody gets anything. This is a one-shot game, with the assurance that A and B will not meet again. A self regarding proponent who believes the responder is also self-regarding will offer $1 and the responder will accept. If a proponent believes that the other player is not self-regarding, he will try to offer the minimum requires to avoid a rejection, namely to adopt the strategy that maximizes his payoff.

· The Dictator Game: this is like the Ultimatum game with the proviso that B cannot refuse, so that A may keep all the money, if he so chooses. A self-regarding individual will offer nothing because the other cannot affect him in any way.

· The Public Goods Game: takes various forms. Here is one. Groups of 4 subjects are formed. Each member is given a private account P with points (say 10), redeemable at the end for real money. The game may have several rounds, each of which consists in the following. Each player can place points in a common account C or keep them. The players are told that the experimenter will double the points in C and then divide them equally among them. So, if everyone puts all the points in C, each will end up with 20 points, with a net gain of 10. However, if Joe puts nothing in C while the others put 10 points each, then Joe will end up with 15 points. Hence, if Joe’s is self-regarding, he’ll contribute nothing. (The players are anonymous and there’s no opportunity to punish defectors). In effect, this game is a version of the Prisoners Dilemma as the following matrix shows.

Cooperate Defect	Cooperate	Defect
	+10	-5
	+15	0

In experiments (mostly on university students all over the world), one observes that:

· In the Ultimatum Game most offers hover about 40%-50% and are accepted; typically, offers below 30% are rejected. If the presenter is known to be non-human, any offer is accepted.

· Third parties witnessing the prisoners’ dilemma and the dictator game engage in altruistic punishment, as long as the cost is not too high.

· In repeated public goods games, most cooperate initially but end up by defecting in the absence of cooperation if unable to punish free riders; moreover, if given the chance to punish defectors, they do so at a cost, ultimately achieving very high levels of cooperation. This occurs even when group composition is constantly changed so that nobody encounters another more than once, which rules out enlightened self-interest in punishing.

In short, instead of favoring homo economicus experimental evidence shows that many players

• engage in strong reciprocity, that is in
1. altruistic cooperation (initially cooperating but eventually defecting if others defect first)
2. altruistic punishment (punishing those who do not display character virtues even at one’s net cost as long as such costs are not too high)
• display some inequality aversion even at a net cost (as long as it isn’t too high), especially if they are victims of inequality.

This contention seems supported by the fact that the punishing of shirkers (even the mere witnessing of it) activates pleasure centers in the brain: revenge is indeed sweet.

However, recent work done in 15 small scale societies around the world complicates the picture considerably, showing that cultural variation is high, probably because people interpret the games in the light of their social practices. For example, if they often engage in communal efforts such as hunting large pray in common, they’ll tend to interpret Ultimatum or Public Goods games in that light and behave accordingly.

Ultimatum Game

· With university students, the mean offer is between 42% and 48%; however, the mean offers in the 15 small scale societies vary between 25% and 75%

· The modal student offer is slightly above 50%; however, in the 15 small scale societies the modal offers vary from 15% to 50%.

· Typically students rejected offers below 40%; however, in some of the 15 small scale societies there were no rejections even of offers of 10% or below 30% (Kazakh, Quichua, Machiguenga), and in some even hyper-fair offers above 50% were rejected (Au and Gnau of Papua New Guinea)

Although the assumption of self-interestedness predicted respondent behavior in half of the societies (where no offers were rejected) it predicted proposer behavior only with respect to students and two groups (Hadza and Sangu farmers), where the offers were close to income-maximizers. Otherwise, offers were higher (even up to 400%) than the expected income-maximizer offers; moreover, risk-aversion fails to explain the proposer behavior because some of these societies are risk-preferring, and the levels of risk-aversion required are implausible (e.g. preferring 4 cents for sure to an expected payoff of $4.5).

Inter-group variations of behavior in the game are statistically correlated to different social practices and levels of market-integration, and this suggest causal links. For example:

· Among the Papua New Guinean tribes of the Au and the Gnau, many offers were above 50% and rejected. The reason is that in Melanesian cultures one achieves high status through gift-giving. Hence, making a large gift is a bid for social dominance and rejecting the bid is a rejection of social subordination.

· The Hadza, a tribe located in Tanzania, made low offers and had high rejection rates, which mirrors the tendency of these small-scale

foragers to share meat, but with a high level of conflict and frequent attempts to hide their catch from the group.

· The Ache, a tribe located in Peru made many offers close to 50% with no rejections. In daily life, the Ache regularly share meat, which is distributed equally among all the households, irrespective of which hunter made the catch.

· The Machiguenga, who until recently did not have personal names, and the Tsimane made low offers which were rarely rejected. These groups cooperate only at the family level, and therefore the anonymity of the players removed fairness considerations

· The Lamalera engage in whale hunting involving the whole village, which elicited fair offers to other anonymous villagers.

· The Mapuche believe that illness and death is caused by the malevolent magic of neighbors and that material wealth is the result of trickery and deals with spirits. Hence they made low offers which were rarely rejected

Intra-group variations are largely unexplained. They are not correlated to age, sex, or social and economic status.

The Dictator Game

Only 3 groups were considered, Horma, Hadza, and Tsimane.

· Mean offers were between 20% and 30% with almost nobody offering zero.

· By contrast, the modal offer among students was zero.

So, the selfishness axiom predicts only student behavior. However, there is evidence that behavior in this game is highly influenced by framing. For example, if the ‘dictator’ can not only offer money, but also take money away from the other, many will take away some.

The Public Goods Game

The game was played in 6 societies. Here too cultural variation is high:

· With university students, the contribution distribution has a U-shape, with primary mode at full defection (no contribution to the common fund) and secondary mode at full cooperation, and very little in the middle; the mean contribution is between 40% and 60%.

· The Machiguenga has the mode at full defection and almost no full contribution, with a mean of 22%.

· Some societies produce an inverted U-shape distribution, with only one mode between 50% and 67% (Ache and Tsimane)

· Some societies have bimodal distribution with one peak between 40% and 50% and the other at full cooperation, with no full defection (Orma, Huinca).

In sum, self-regardedness fails to predict the actual outcome; strong reciprocity works better but one must keep an eye on cultural variations.