Game Theory: Cooperators, Loners, Free Riders, and Punishers

James Fowler is a new kind of political scientist. Specializing in genopolitics, the genetic basis of political behavior, and the evolution of cooperation, he melds the social with the biological, pushing the boundaries of his field to discover, for example, that smoking, obesity, and happiness spread within social networks, and that genes affect voting behavior. A professor at the University of California, San Diego, Fowler is famous among students for publishing the first scientific evidence to support the "Colbert bump." His new book, co-written with sociologist Nicholas Christakis, is Connected: The Surprising Power of Social Networks and How They Shape Our Lives,

Review by Luc Reid

In their book Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives, sociologist Nicholas Christakis and political scientist James Fowler look at what it means to be a human being in terms of our interpersonal networks. One of the topics they take up is an examination of how selfishness, cooperation, and altruism interact, which helps answer the question in the title: can we expect others to help us?

Christakis and Fowler take results from experiments around the world with three games. In the “Ultimatum Game,” two people are given an amount of money (for instance, ten dollars).

Person 1 makes an offer to split it with the other, offering anything from a penny to a 50/50 split to handing over the whole amount. Person 2 decides to reject or accept the offer. If Person 2 rejects the offer, neither person gets anything.

The “Dictator Game” is similar, except that any offer is automatically accepted. All the power lies with Person 1.

In the “Trust Game,” Person 1 can give any amount to Person 2, and that amount triples, at which point Person 2 can give any amount back. If both cooperate completely, they each get more than the original amount. If they don’t, someone gets screwed.

I won’t go into the experimental findings in detail, but instead will head straight for the conclusions Christakis, Fowler, and others draw from the results.

Based on the mixture of selfishness, cooperation, trust, mistrust, and other attitudes demonstrated by subjects in these experiments, they identify three types of people: cooperators, loners, and free riders.

Cooperators tend to trust more, are more helpful to others, and are dependent on other people trusting and helping in return. Loners tend not to trust and try not to depend on anyone else. Free riders take advantage of cooperators to get whatever they can for themselves without offering anything in return.

A cooperator in the midst of other cooperators thrives. A cooperator who runs into too many free riders gets screwed. A loner is less successful than others if everyone else is successfully cooperating, but isn’t in danger of being taken advantage of by free riders. A free rider thrives when cooperators let things go, but runs into trouble with a sort of cooperator sub-type that Christakis and Fowler dub “Punishers.” Punishers are willing to exert some effort to penalize people for not cooperating or for taking advantage of the system.

In the ultimatum or dictator game, a cooperator might offer half or close to half of the money to the other person. A loner in the trust game will assume the other person is going to take advantage and act defensively. A free rider will take the most money available regardless of consequences to the other player. A punisher in the ultimatum game will refuse an offer that seems too low even though this would mean both players lose out.

What’s fascinating to me is that according to Christakis and Fowler, a society is made up of all of these types, but the proportions of each are constantly shifting. There appear to be times and places where cooperators spread, which might eventually attract free riders, which in turn will attract punishers and perhaps turn some of the cooperators into loners. If loners are everywhere, then some might band together and be more successful by cooperation, starting the cycle over. During each separate phase of this cycle, which might last for some time, there are different opportunities and dangers, and the question of whether help is likely to be available is answered differently.

So when looking for help in our lives, there are questions we can ask ourselves. Are we given to cooperation, or do we tend to do things on our own? What about the people around us? And whether or not a person tends to help in one area suggests a lot about whether that person is likely to help in another.

For instance, a person who gives money to public radio is also more likely to volunteer to help you move or to give you directions if you’re lost. A person who works in a kind of job that emphasizes getting as much as you can, like a stockbroker or auto salesperson, is less likely to trust and offer help to others – though of course it’s inaccurate to make blanket statements about people on this matter; these are just general observations that are often true.

Regardless, making these kinds of observations about yourself and the people you’re connected with can help provide insight both about what you’re contributing and what you can expect from others.

The Nelson Touch Blog: Team Incentives and the Free Rider Problem

Team incentives, where an individual’s compensation is based on the team’s performance, are notoriously difficult to implement. Yet more and more work in companies large and small is being done through formal or informal teams. What do we need to know in order to design better team incentives?




Standard economic theory is a good place to start (though it will not provide all the answers). Economic theory assumes that people prefer leisure to work and are self-interested. Team incentives therefore fall victim to the “free rider” problem.

If all team members are rewarded for the team’s output, then there is little incentive for a self-interested, leisure-seeker to contribute toward the team goals. Since the “shirker” cannot be excluded from the reward, he becomes a free rider – enjoying the rewards without adding any effort. Game theory predicts that all team members look around and decide that their best strategy is not to work either, so the team ends up not working at all. The group incentive has led to a completely undesirable result.

Of course, this is a rather extreme portrayal, but it drives home the point and illustrates why any good compensation professional will tell you “be careful what you pay for.” There are a few ways of dealing with the free rider problem.

The simplest solution is to introduce a way of monitoring effort so that you share in the reward only if there is evidence that you have worked hard enough or well enough. This is what performance management is all about. The monitoring can be done by the firm (e.g., the manager) or by other members of the team. The latter is only practical if the team is small and each member’s effort is observable and measurable.

The situation can be saved if there is repeated interaction among the team members. If there are multiple opportunities for the team to work together for a reward in the future, then team members will be more likely to co-operate in the current project and work.  If they don’t, they may lose future earning opportunities. There may be reputational consequences for poor individual effort. This works out well if teams are formal (i.e., not ad hoc and one-time) and long-lived.

Another dimension to this is if there are social sanctions available. Groups that work together might also “play” together – i.e., have relationships beyond the confines of the team situation. Members can put pressure on team-mates to shape up or ship out.

When team members are close-knit, they internalize each others’ welfare. This builds a positive, co-operative, stable equilibrium. This approach jibes with Jon Katzenbach’s observation of high-performing teams (what he calls “real teams”): that team members become invested in each others’ development and well-being.

Given the above discussion, we can say that the factors that influence whether team incentives will work or not include team longevity, size and composition.

The longer a team stays together, the more powerful the measures of peer pressure, social sanction and internalized welfare.

The larger the team gets, the less members are able to monitor each other, reach a collusive equilibrium, exert social sanctions or internalize each others’ welfare. Other, external factors will play a more prominent role. Also, there will be fewer opportunities to measure relative performance since there will be fewer similar teams for comparison.

Team composition is an important factor. Allowing teams to form autonomously has risks: the team may play well internally but may not play well with other teams. On the other hand, teams of like-minded individuals who have self-selected into the team knowing who they will be working with are likely to perform better. Heterogeneity in team composition is a good thing and is supported by Katzenbach’s notion of complementary skills.

So what is to be done with respect to team incentives? You clearly have to be very careful to avoid the free rider problem. Ownership can play a large role, as can other ways to build and sustain high commitment to a team’s objectives. Even though everyone is not the perfectly rational economic agent that economic theory assumes, you still need to model the game-theoretic or strategic outcomes in order to thwart team members’ efforts at “gaming” the team incentive.

Richard Dawkins: Game Theory: Tit-For-Tat

Richard Dawkins on Game Theory

http://www.youtube.com/watch?v=48EWLj3gIJ8

From yee Wiki:

Tit for tat is an English saying meaning "equivalent retaliation". It is also a highly effective strategy in game theory for the iterated prisoner's dilemma. The strategy was first introduced by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. Notably, it was (on both occasions) both the simplest strategy and the most successful.

An agent using this strategy will first cooperate, then subsequently replicate an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is similar to superrationality and reciprocal altruism in biology.

Explaining reciprocal altruism in animal communities

Studies in the prosocial behaviour of animals, have led many ethologists and evolutionary psychologists to apply tit-for-tat strategies to explain why altruism evolves in many animal communities. Evolutionary game theory, derived from the mathematical theories formalised by von Neumann and Morgenstern (1953), was first devised by Maynard Smith (1972) and explored further in bird behaviour by Robert Hinde. Their application of game theory to the evolution of animal strategies launched an entirely new way of analysing animal behaviour.



Reciprocal altruism works in animal communities where the cost to the benefactor in any transaction of food, mating rights, nesting or territory is less than the gains to the beneficiary. The theory also holds that the act of altruism should be reciprocated if the balance of needs reverse. Mechanisms to identify and punish "cheaters" who fail to reciprocate, in effect a form of tit for tat, is an important mechanism to regulate reciprocal altruism.

What's Fair? The Ultimatum Game

Sometimes I feel like I'm doing more than my fair share of work. I am reminded of Behavioral Economics' Ultimatum Game.

If you say so : Extensive form representation of a two proposal ultimatum game. Player 1 can offer a fair (F) or unfair (U) proposal; player 2 can accept (A) or reject (R).

The Ultimatum Game

From ye Wiki: The ultimatum game is a game often played in economic experiments in which two players interact to decide how to divide a sum of money that is given to them. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. If the second player rejects, neither player receives anything. If the second player accepts, the money is split according to the proposal. The game is played only once so that reciprocation is not an issue.

Equilibrium analysis

For illustration, we will suppose there is a smallest division of the good available (say 1 cent). Suppose that the total amount of money available is x.

The first player chooses some amount p in the interval [0,x]. The second player chooses some function f: [0, x] → {"accept", "reject"} (i.e. the second chooses which divisions to accept and which to reject). We will represent the strategy profile as (p, f), where p is the proposal and f is the function. If f(p) = "accept" the first receives p and the second x−p, otherwise both get zero. (p, f) is a Nash equilibrium of the ultimatum game if f(p) = "accept" and there is no y > p such that f(y) = "accept" (i.e. player 2 would reject all proposals in which player 1 receives more than p). The first player would not want to unilaterally increase his demand since the second will reject any higher demand. The second would not want to reject the demand, since he would then get nothing.

There is one other Nash equilibrium where p = x and f(y) = "reject" for all y>0 (i.e. the second rejects all demands that gives the first any amount at all). Here both players get nothing, but neither could get more by unilaterally changing his / her strategy.

However, only one of these Nash equilibria satisfies a more restrictive equilibrium concept, subgame perfection. Suppose that the first demands a large amount that gives the second some (small) amount of money. By rejecting the demand, the second is choosing nothing rather than something. So, it would be better for the second to choose to accept any demand that gives her any amount whatsoever. If the first knows this, he will give the second the smallest (non-zero) amount possible.

Experimental results

In industrialized cultures, people offer "fair" (i.e., 50:50) splits, and offers of less than 20% are often rejected. One limited study on monozygotic and dizygotic twins claims that genetic variation can affect reactions to unfair offers, though the study failed to employ actual controls for environmental differences.

Explanations

The highly mixed results (along with similar results in the Dictator game) have been taken to be both evidence for and against the so-called "Homo economicus" assumptions of rational, utility-maximizing, individual decisions. Since an individual who rejects a positive offer is choosing to get nothing rather than something, that individual must not be acting solely to maximize his economic gain, unless one incorporates economic applications of social, psychological, and methodological factors (such as the observer effect). Several attempts to explain this behavior are available. Some authors suggest that individuals are maximizing their expected utility, but money does not translate directly into expected utility. Perhaps individuals get some psychological benefit from engaging in punishment or receive some psychological harm from accepting a low offer. It could also be the case that the second player, by having the power to reject the offer, uses such power as leverage against the first player, thus motivating him to be fair.

The classical explanation of the ultimatum game as a well-formed experiment approximating general behaviour often leads to a conclusion that the rational behavior in assumption is accurate to a degree, but must encompass additional vectors of decision making. However, several competing models suggest ways to bring the cultural preferences of the players within the optimized utility function of the players in such a way as to preserve the utility maximizing agent as a feature of microeconomics. For example, researchers have found that Mongolian proposers tend to offer even splits despite knowing that very unequal splits are almost always accepted. Similar results from other small-scale societies players have led some researchers to conclude that "reputation" is seen as more important than any economic reward.

Others have proposed the social status of the responder may be part of the payoff. Another way of integrating the conclusion with utility maximization is some form of inequity aversion model (preference for fairness). Even in anonymous one-shot settings, the economic-theory suggested outcome of minimum money transfer and acceptance is rejected by over 80% of the players.

An explanation which was originally quite popular was the "learning" model, in which it was hypothesized that proposers’ offers would decay towards the sub game perfect NE (almost zero) as they mastered the strategy of the game. (This decay tends to be seen in other iterated games). However, this explanation (bounded rationality) is less commonly offered now, in light of empirical evidence against it.

It has been hypothesised (e.g. by James Surowiecki) that very unequal allocations are rejected only because the absolute amount of the offer is low. The concept here is that if the amount to be split were ten million dollars a 90:10 split would probably be accepted rather than spurning a million dollar offer.

Essentially, this explanation says that the absolute amount of the endowment is not significant enough to produce strategically optimal behaviour. However, many experiments have been performed where the amount offered was substantial: studies by Cameron and Hoffman et al. have found that the higher the stakes are the closer offers approach an even split, even in a 100 USD game played in Indonesia, where average 1995 per-capita income was 670 USD.

Rejections are reportedly independent of the stakes at this level, with 30 USD offers being turned down in Indonesia, as in the United States, even though this equates to two week's wages in Indonesia

Neurologic explanations

Generous offers in the ultimatum game (offers exceeding the minimum acceptable offer) are commonly made. Zak, Stanton & Ahmadi (2007) showed that two factors can explain generous offers: empathy and perspective taking. They varied empathy by infusing participants with intranasal oxytocin or placebo (blinded). They affected perspective-taking by asking participants to make choices as both player 1 and player 2 in the ultimatum game, with later random assignment to one of these. Oxytocin increased generous offers by 80% relative to placebo. Oxytocin did not affect the minimum acceptance threshold or offers in the dictator game (meant to measure altruism). This indicates that emotions drive generosity.

Rejections in the ultimatum game have been shown to be caused by adverse physiologic reactions to stingy offers. In a brain imaging experiment by Sanfey et al., stingy offers (relative to fair and hyperfair offers) differentially activated several brain areas, especially the anterior insular cortex, a region associated with visceral disgust. If Player 1 in the ultimatum game anticipates this response to a stingy offer, they may be more generous.

An increase in rational decisions in the game has been found among experienced Buddhist meditators. fMRI data show that meditators recruit the posterior insular cortex (associated with interoception) during unfair offers and show reduced activity in the anterior insular cortex compared to controls.

People whose serotonin levels have been artificially lowered will reject unfair offers more often than players with normal serotonin levels.

This is true whether the players are on placebo or are infused with a hormone that makes them more generous in the ultimatum game.

People who have ventromedial frontal cortex lesions were found to be more likely to reject unfair offers. This was suggested to be due to the abstractness and delay of the reward, rather than an increased emotional response to the unfairness of the offer.

Evolutionary game theory

Other authors have used evolutionary game theory to explain behavior in the ultimatum game. Simple evolutionary models, e.g. the replicator dynamics, cannot account for the evolution of fair proposals or for rejections. These authors have attempted to provide increasingly complex models to explain fair behavior.

Sociological applications

The ultimatum game is important from a sociological perspective, because it illustrates the human unwillingness to accept injustice. The tendency to refuse small offers may also be seen as relevant to the concept of honour.

The extent to which people are willing to tolerate different distributions of the reward from "cooperative" ventures results in inequality that is, measurably, exponential across the strata of management within large corporations. See also: Inequity aversion within companies.

Some see the implications of the ultimatum game as profoundly relevant to the relationship between society and the free market, with Prof. P.J. Hill, (Wheaton College (Illinois)) saying:
I see the [ultimatum] game as simply providing counter evidence to the general presumption that participation in a market economy (capitalism) makes a person more selfish.
History

The first ultimatum game was developed in 1982 as a stylized representation of negotiation, by Güth, Schmittberger, and Schwarze. It has since become a popular economic experiment, and was said to be "quickly catching up with the Prisoner's Dilemma as a prime showpiece of apparently irrational behavior" in a paper by Martin Nowak, Karen M. Page, and Karl Sigmund.

Variants

In the "competitive ultimatum game" there are many proposers and the responder can accept at most one of their offers: With more than three (naïve) proposers the responder is usually offered almost the entire endowment (which would be the Nash Equilibrium assuming no collusion among proposers).

In the "ultimatum game with tipping", a tip is allowed from responder back to proposer, a feature of the trust game, and net splits tend to be more equitable.

The "reverse ultimatum game" gives more power to the responder by giving the proposer the right to offer as many divisions of the endowment as they like. Now the game only ends when the responder accepts an offer or abandons the game, and therefore the proposer tends to receive slightly less than half of the initial endowment.

Robert Aumann's Blackmailer Paradox appears to be a repeated game in which the ultimatum game is played many times by the same players for high stakes.

The pirate game illustrates a variant with more than two participants with voting power, as illustrated in Ian Stewart's "A Puzzle for Pirates".