Altruistic Hedonic Games

Abstract

Hedonic games are coalition formation games in which players have preferences over the coalitions they can join. For a long time, all models of representing hedonic games were based upon selfish players only. Among the known ways of representing hedonic games compactly, we focus on friend-oriented hedonic games and propose a novel model for them that takes into account not only the players’ own preferences but also their friends’ preferences. Depending on the order in which players look at their own or their friends’ preferences, we distinguish three degrees of altruism: selfish-first, equal-treatment, and altruistic-treatment preferences. We study both the axiomatic properties of these games and the computational complexity of problems related to various common stability concepts.

Altruism in coalition formation games

“…Based on friend-oriented preferences, Nguyen et al [1] introduced altruistic hedonic games (AHGs) where agents gain utility not only from their own satisfaction but also from their friends' satisfaction. However, Nguyen et al [1] specifically considered hedonic games only, which require that an agent's utility only depends on her own coalition.…”

“…Based on friend-oriented preferences, Nguyen et al [1] introduced altruistic hedonic games (AHGs) where agents gain utility not only from their own satisfaction but also from their friends' satisfaction. However, Nguyen et al [1] specifically considered hedonic games only, which require that an agent's utility only depends on her own coalition. In their interpretation of altruism, the utility of an agent is composed of the agent's own valuation of her coalition and the valuation of all this agent's friends in this coalition.…”

“…In their interpretation of altruism, the utility of an agent is composed of the agent's own valuation of her coalition and the valuation of all this agent's friends in this coalition. While Nguyen et al [1] used the average when aggregating some agents' valuations, Wiechers and Rothe [5] proposed a variant of altruistic hedonic games where some agents' valuations are aggregated by taking the minimum.…”

“…For the coalition structures = {{1, 2, 3}, {4}} and = {{1, 2, 4}, {3}}, it is clear that player 1 is indifferent between coalitions {1, 2, 3} and {1, 2, 4} under friend-oriented preferences, as both coalitions contain 1's only friend (player 2) and one of 1's enemies (either 3 or 4). Under altruistic hedonic preferences [1], however, player 1 behaves altruistically to her friend 2 (who is friends with 3 but not with 4) and therefore prefers {1, 2, 3} to {1, 2, 4}. Now, consider the slightly modified coalition structures = {{1}, {2, 3}, {4}} and = {{1}, {2, 4}, {3}}.…”

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Nguyen et al (2016) introduced altruistic hedonic games in which agents' utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions.

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