Fairness In Game Theory

Overview | What Is Fairness? | Fairness In Game Theory | Retaliation and Reciprocity | William Baumol's Fairness Assumption | The Ultimatum Game Under Baumol's Fairness Assumption | Fairness Theory Homepage

Is it fair to assume that players are entirely self-interested?

In the neo-classical economic school of thought, the unit of analysis for economic well-being is the individual, usually referred to as homo economicus. It is assumed that this individual will make economic decisions solely for himself and seek to maximize his personal utility, rather than taking anyone else's utility into consideration. However, we must call these neo-classical assumptions into question. Can we presume that there are only selfish and self-improvement seeking individuals within the economic arena? Perhaps we should make the argument that one's personal utility is a function of others' utilities as well. Hence, this page will demonstrate that there is more involved in the analysis of economic games than simply the individual's selfish motives.

People sometimes take others' actions into consideration...

The following are general behavioral rules for those who act out of fairness:

• They are kind to those who act kindly towards them.
• They are hurtful and retaliatory towards those who are unkind.
• People may not only refuse to help those who are unkind, but will actually sacrifice their payoffs to hurt those who are being unfair.

It is typically thought that the player in a game, such as those which follow, will reason to the extent which allows him to achieve the best result for himself. Disregarding all resulting consequences for the other players, this individual is assumed to be greedy. However, to identify this player as selfish may not always be acceptable. A player may consider the well-being of another in his decision, or act based on his take on the fairness of the situation. The results of these games, therefore, would change drastically in contrast to the previous assumption that the player is completely self-interested.

• The Ultimatum Game

The Ultimatum Game is a situation in which a set of individuals must decide upon the division of a fixed sum of money. The game consists of two players, the proposer, who extends an offer to the decider, who can either accept or decline that offer. In the event that the deal is rejected, neither of the two players receives payment.

One would normally assume that the player should accept any offer, considering that some form of payoff is better than none at all. But, when one throws the concept of fairness into the equation, the player may gain more satisfaction from receiving nothing than from accepting an unfair deal.

The extent to which people are willing to sacrifice their potential "material gains" to maintain fairness is largely dependent on the size of such gains. For instance, in a situation where the division of money is $0.90 to the proposer and $0.10 to the decider, the decider will most likely give up his share entirely to "punish" the proposer for suggesting such an unfair offer (assuming that both players receive nothing if the offer is declined). However, if the stakes had been increased from the limits of a dollar to a division of $9 million and $1 million, respectively, then the decider may be far less willing to sacrifice that amount.

Societal Research

Joseph Henrich, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, Herbert Gintis, and Richard McElreath all conducted research dealing with the ultimatum game (and others) among 15 culturally distinct countries. In the article, In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies, the reader gains varied insight as to how the members of these cultures responded differently - mostly how their actions contrasted to what they had been predicted to do.

In general, the results of these experiments contradicted the traditional models typically held for these games. Offers seemed to exceed the norm, whereas rejection rates of those "high" offers were also quite frequent. As indicated in this study, distinct cultures hold varying interpretations of "gift-giving." The importance of one's reputation within society seems to have played a significant role in the players' actions as well.

The following conclusions were made as a result of this experiment, and are stated verbatim as they appear in the text:

While economists should not abandon the rational-actor framework, they should make revisions.

1. The canonical model of the self-interested material payoff-maximizing actor is systematically violated.
2. Preferences over economic choices are not exogenous as the canonical model would have it, but rather are shaped by the economic and social interactions of everyday life.
3. The connection between experimental behavior and the structure of everyday economic life should provide an important clue in revisiong the canonical model of individual choice behavior.

• Prisoner's Dilemma versus Prisoner's Non-dilemma

Another game that may bring homo economicus into question is the Prisoner's Dilemma Game. In this two-player game, players can opt either to cooperate with a decision made by the other player or defect. Based on the knowledge of the other player's move, player 2 can respond kindly to the kind action of his counterpart, or respond hostily if player 1 is acting selfishly to maximize his own personal payoff. People sometimes cooperate, but if each expects the other player to defect, then they both will, reducing both of their payoffs.

Players tend to make decisions that will result in Nash equilibria / fairness equilibria. However, supposing that one player is forced to choose to cooperate, perhaps via contract, the other player will tend to completely disregard the well-being of that player and focus on his own utility. People tend to differentiate between genuine and forced behavior. No one is grateful to someone for doing something that he must. Thus, in this Prisoner's Non-dilemma, one will not act kindly if he views the other player as unkind as coerced in his action.