Loyalty in Cardinal Hedonic Games

Abstract

A common theme of decision making in multi-agent systems is to assign utilities to alternatives, which individuals seek to maximize. This rationale is questionable in coalition formation where agents are affected by other members of their coalition. Based on the assumption that agents are benevolent towards other agents they like to form coalitions with, we propose loyalty in hedonic games, a binary relation dependent on agents' utilities. Given a hedonic game, we define a loyal variant where agents' utilities are defined by taking the minimum of their utility and the utilities of agents towards which they are loyal. This process can be iterated to obtain various degrees of loyalty, terminating in a locally egalitarian variant of the original game. We investigate axioms of group stability and efficiency for different degrees of loyalty. Specifically, we consider the problem of finding coalition structures in the core and of computing best coalitions, obtaining both positive and intractability results. In particular, the limit game possesses Pareto optimal coalition structures in the core.