Rabin fairness

Rabin fairness is a fairness model invented by Matthew Rabin. It goes beyond the standard assumptions in modeling behavior, rationality and self-interest, to incorporate fairness. Rabin's fairness model incorporates findings from the fields of economics and psychology fields to provide an alternative utility model. Fairness is one type of social preference.

Past utility models incorporated altruism or the fact that people may care not only about their own well-being, but also about the well-being of others. However, evidence indicates that pure altruism does not occur often, contrarily most altruistic behavior demonstrates three facts (as defined by Rabin) and these facts are proven by past events. Due to the existence of these three facts, Rabin created a utility function that incorporates fairness.:

Rabin formalized fairness using a two-person, modified game theory matrix with two decisions (a two by two matrix), where i is the person whose utility is being measured. Furthermore, within the game theory matrix payoffs for each person are allocated. The following formula was created by Rabin to model utility to include fairness:

Where:

The fairness model implies that if player j is treating player i badly, if ƒ_j(b_j, c_i) < 0, then player i wishes to treat player j badly as well by choosing an action, a_i, that is low or negative. However, if player j is treating player i kindly, ƒ_j(b_j, c_i) > 0, then player i will act kindly towards player j, as well (For more in depth examples see Rabin (1993)).

Rabin also used the fairness model as a utility function to determine social welfare. Rabin used a game theory "Grabbing Game" which posited that there are two people shopping, with two cans of soup left. The payoffs for each are given as follows, where player i's payoffs are on the left of each pair and player j's payoffs are on the right of each pair:

If both grab or both share, each player i and j get one can of soup. However, one grabs, and the other does not, then the person who grabbed gets both cans of soup. There is a Nash Equilibrium present of (grab, grab). Moreover, applying Rabin's fairness model (grab, grab) will always be a fairness equilibrium but for small values of x the cooperative choice (share, share) will Pareto dominate (grab, grab). The reasoning behind this is that if the two people both grab for and therefore fight over the cans, the angriness and bad tempers that arise are likely to outweigh the importance of receiving the cans. Therefore, while (Grab, Grab) and (Share, Share) are fairness equilibria when material payoffs are small, (Share, Share) will dominate (Grab, Grab) since people are affected by the kindness, which increases utility, or unkindness, which decreases utility, of others. This example could be generalized further to describe the allocation of public goods.

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