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. Of course, in practice homo economicus often adopts 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.

· 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 senses 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, from a purely game-theoretical perspective what counts as payoff depends on the nature of the game and not on the intentions, if any, of the agent.

When it comes to beings that form intentions, another point must be considered. Allegedly, a friend told Hobbes that psychological egoism must be false because Hobbes gave money to a beggar. Hobbes replied that he did it because otherwise he would have felt guilty, so that the motive was not helping the beggar but avoiding an unpleasant emotion. Was Hobbes’ defense satisfactory? It depends; a feeling of guilt at not helping the beggar is exactly what we would expect from an altruist, but if the motive of the action must be concern for the beggar aside from any guilt considerations, then Hobbes’ reply is good. Almost certainly, we tend to act from mixed motives, both out of real concern for others and from our desire to avoid guilt, which is sufficient to produce psychological altruism.

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. Hence, social preferences leading to, say strong reciprocity, are irrational, and 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.

The main problem with rational egoism is that it fails to produce optimal equilibriums in Prisoner’s Dilemma situations and dismisses social preferences as irrational by fiat. This open the problem of determining the formal criteria of rational preference schemes; notice that social preferences satisfy transitivity.

Prisoners Dilemma. Consider the following story. Two criminals are arrested and the prosecutor has not enough evidence to convict either of a serious crime unless one or both confesses; however, the two criminals do not know this. Hence he tells one of prisoners: “If you confess and the other guy does not, I’ll grant you immunity and you walk free. If the other confesses and you don’t, I shall make sure that you get a heavy sentence. If neither of you confesses I shall settle for misdemeanor charges, with the result that you will pay a small fine and walk free. If both of you confess, I shall charge both with a felony but also argue for shorter sentences than you would get if the other guy squeals and you do not.” Keeping in mind that the game is one of complete knowledge, what should a prisoner do?

Here is the strategy matrix, with S representing “keeping silent” and T “talk”, +10 the utility of walking free, -10 that of a heavy sentence, -5 that for felony charges but with shorter sentence, and -1 that for misdemeanor charges:

Player B
Player A		S	T
	S	-1	-10
	T	+10	-5

The game is neither a coordination nor a zero-sum game, but it is dominance solvable: T dominates S; consequently, (T,T) provides a dominance equilibrium: no matter what the other does, it’s better to talk: if you talk and the other does not, you walk free (+10 payoff); if you talk and the other does as well, you get a -5 payoff. At all cost you want to avoid keeping silent when the other confesses. Rational egoism prevents both from following (S, S) (both keep silent), which would provide a better outcome for the two together. This is why this game is called “Prisoners Dilemma”: rational egoism leads would lead to common failure. One can think of Prisoners Dilemma in terms of cooperation (cooperating with the other by keeping silent) and defection (going at it alone by confessing). Notice two things:

1. If the players are self-regarding communication does not solve the problem: even if I know that you will not confess, it is still in my self-interest to confess.

2. Even finite iteration of the game need not change its outcome. For example, suppose I know that the game will be played 10 times. Then I know that in the tenth round I should confess, independently of what happened in the ninth round. Hence, in the eighth round I should confess because what happens in the ninth does not affect what happens in the tenth, and so on. In other words, backward induction demands that I confess.

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

A 2-person ultimatum game can be constructed as follows: each can contribute 0≤ X_i ≤1(i has value 1 or 2, indicating whose contribution X is), and each gets back n(X₁ + X₂). As long as ½<n<1, the game is a Prisoners Dilemma.

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. Rejectors experience anger and disapproval, and the brain centers associated with anger and disgust are activated; even after a one hour cooling period the rejector’s emotiona reaction and behavior are the same. 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. People punish even when transgressors are punished after the game is over.

· 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.

Analogous results have been obtained in other games such as the gift exchange game.

The pervasive presence of costly punishment

· ties well with the fact that the punishing of shirkers (even the mere witnessing of it) activates pleasure centers in the brain: revenge is indeed sweet.

· shows that the “natural” type of punishment is retributive and not consequentialist.

Note however, that symbolic punishment (so-and-so was stingy and selfish announced in public, for example) is about as effective as punishment that reduces benefits.

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-interestededness 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.

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.

All of the above does not show that results in experimental settings are ipso facto transferable to real life (non-experimental) settings; for example, people who reported they never give to charity, allocated 60% of their endowment in experimental setting. Nevertheless, results in experimental setting can be used to predict behavior in real life; for example, among Brazilian shrimpers, cooperation in public game settings predicts cooperation is real life –avoidance of smaller holes in the buckets used for catching shrimp).

So, one can reasonably assume that most societies in which interaction goes beyond kin a notable percentage is constituted by strong reciprocators who, in the absence of centralized authority, see to it that social deviancy is maintained low. This can be seen in ethnographic foraging societies, which are taken to be similar to late Pleistocene ones.

But can we infer from ethnographic foragers to pre-Holocene ones?

Objection: ethnographic foragers have been marginalized by more powerful societies. Before Holocene they had the pick of the best environments. (Service, Kelly).

Reply: Late Pleistocene climate variability, migrations, and wars.

Boehm: survey of ethnographic hunter gatherer societies that were (are)

· Without animal husbandry or agriculture, dependency outsiders (e.g., missions or modern states), trading links with horticulturalists, food storing, sedentary life

· With mobile life (no year round villages), hunting/gathering what’s environmentally available, emphasis on eating large mammals, band of 25/35 people on average. (Note that what’s average, i.e., mean, need not be what’s typical, i.e., normalized weighted average).

Such societies, independently of location, are highly egalitarian (among hunters), without any centralized authority, and exercise social control of the following transgressions:

· free riding and theft

· intimidation through sorcery, threat of physical violence, murder, or psychotic aggression, resulting in bossing

· sexual transgression such as incest or adultery

· betrayal of group to outsiders

· violation of taboo.

Social control is achieved by means that from cool greetings, to ridiculing, to physical violence and killing.

Since strong reciprocators pay a cost that egoistical people avoid, apparently adopting strategies that are dominated, how can they have evolved to be successful?