October 20, 2009

Altruism in Game Theory


Most if not all microeconomic models assume that individuals only care about what increases their utility. In fact, this notion goes back to Adam Smith, who believes that it is individuals' self-interests that keep the economy going. Even the most recent evidence on altruism, an exception to the notion of the self-interested homo economicus, show that altruistic people are not really motivated by generosity per se. According to a paper by Matthew Rabin of University of California-Berkeley, people who seemed to be altruistic are so only to altruistic people; they are similarly motivated to hurt people who hurt them. This concept of "fairness equilibrium" is the revolutionary concept that is introduced by Rabin into game theory:

"People like to help those who are helping them, and to hurt those who are hurting them. Outcomes reflecting such motivations are called fairness equilibria. Outcomes are mutual-max when each person maximizes the other's material payoffs, and mutual-min when each person minimizes the other's payoffs. It is shown that every mutual-max or mutual-min Nash equilibrium is a fariness equilibrium."

In other words, for Rabin:

"If somebody is being nice to you, fairness dictates that you be nice to him. If somebody is being mean to you, fairness allows--and vindictiveness dictates--that you be mean to him."

Rabin's revolutionary idea comes into play when he contends that people are willing to sacrifice their own material well-being to either help those who are kind or hurt those who are unkind, and that these two stylized facts have greater effect on individual's behavior because as it will turn out, the material cost of such sacrifices becomes smaller.

The implications of Rabin's study are similarly interesting. His ideas create issues that do not arise in the simple two-person, normal-form, complete-information games. The implications are more complex if an individual is given the choice of helping everybody or hurting everybody. A classic example that Rabin discussed is how much an individual will contribute to a public good--should she contribute to reward those who have contributed, or should she not contribute to punish those who have not contributed? Another interesting implication is if we extend the idea to sequential games. In particular, fairness equilibrium may change the motivations of players at a certain stage of the game: a first-mover may choose some action that will compel another player to regard him positively (or negatively).

Rabin's idea could help explain why if you and your wife are facing a prisoners' dillema and you're willing to sacrifice yourself by not squealing. It's the same reason why your wife will not squeal also. Therefore, we find another Nash equilibrium different from the standard Nash equilibrium solution to the prisoners' dilemma game: both prisoners are better off squealing.

Reference:
Matthew Rabin. 1993. "Incorporating fairness into game theory and economics." American Economic Review 63(5):1281-302.