Generalized Utility Describing Cooperation and Fairness

In this paper we show that for the case of two subjects the inequity-aversion utility coincides with the social-welfare utility that weights egoistic preferences, Hick optimality and maximin fairness. We also compare the generalizations of the inequity-aversion and social-welfare utilities to the case of more than two players and show that these two utilities are generalized in different ways. Additionally to that we propose a new way to generalize a two subjects utility to the case of more than two subjects. The new way of the generalization ensures that neither the cooperative nor the fairness terms will dominate as the size of the group grows. The proposed generalization also makes the utility function less sensitive to the payoff of one player as the size of the group grows. Finally, we introduce a second type of fairness to model decisions in the proposer-responder settings more accurately.