Analysis of the core under inequality-averse utility functions

In this paper, we study cooperative games with the players whose pref- erences depend on all players’ allocations, which we refer to as the social preferences. The social preferences we study in this paper are represented by the utility functions proposed by Fehr and Schmidt (1999) or the util- ity functions proposed by Charness and Rabin (2002). First, we define and characterize the cores, which are the same as the standard core except that the utility functions are the Fehr-Schmidt or the Charness-Rabin type. We show that the Fehr-Schmidt type core becomes smaller if the players become more envious and that it may become larger or smaller if the players become more compassionate. We also show that the Charness-Rabin type core be- comes smaller if the players pay more attention to care about the minimal allocation and that it may become larger or smaller if the players pay more attention to care about the social welfare. Moreover, we analyze the alpha- core and the beta-core of the cooperative games consisting of players with these types of social preferences, as well as a new core concept that takes ac- count of networks among the players. We show that the Fehr-Schmidt type core is the smallest among these cores and that the alpha-core coincides with the beta-core under the Fehr-Schmidt utility functions.