Scale-and Shift-Invariances Explain Two-Player Fehr-Schmidt Fairness Utility Function

In a recent paper [2], it was shown that people’s behavior in simple two-person economic games can be quantitatively explained by using Fehr-Schmidt fairness utility function, i.e., by assuming that a person chooses a strategy for which the following quantity attains the largest possible value: x1 − α · max(x2 − x1, 0) − β · max(x1 − x2, 0), where x1 is this person’s monetary gain and x2 is the gain of the other player. The Fehr-Schmidt utility function has an intuitive explanation, as an approximate expression that captures such feelings as envy and guilt. In [3], it was shown that for an arbitrary number of agents, the corresponding Fehr-Schmidt utility function can be derived from reasonable assumptions such as monotonicity, additivity, etc. In this paper, we show that for the case of two players, already simple invariance requirements uniquely determine this function. Mathematics Subject Classification: 91C99, 91B16, 91B14, 20-xx