Additively Separable Hedonic Games with Social Context

Abstract

In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

Altruistic Hedonic Games

“…Based on the social context games (Ashlagi et al, 2008) described in Section 2.1.1, Monaco, Moscardelli, and Velaj (2018) introduced social context hedonic games (which, in fact, are nonhedonic games). Such games are based on additively separable utilities, an altruism factor, and a social network among the players.…”

Thou Shalt Love Thy Neighbor as Thyself When Thou Playest: Altruism in Game Theory

“…Remotely related is the work ofMonaco, Moscardelli, and Velaj (2018; who study "hedonic games with social context" (which, in fact, are nonhedonic games based on additive separable utilities, an altruism factor, and a social network, and the players' utilities are the sum of their own utilities and the utilities of their friends in the network, the latter weighted by the altruism factor) as well as modified fractional hedonic games (which behave qual-…”