Inefficiency of Games with Social Context

Abstract

Abstract. The study of other-regarding player behavior such as altruism and spite in games has recently received quite some attention in the algorithmic game theory literature. Already for very simple models, it has been shown that altruistic behavior can actually be harmful for society in the sense that the price of anarchy may increase as the players become more altruistic. In this paper, we study the severity of this phenomenon for more realistic settings in which there is a complex underlying social structure, causing the players to direct their altruistic and spiteful behavior in a refined player-specific sense (depending, for example, on friendships that exist among the players). Our findings show that the increase in the price of anarchy is modest for congestion games and minsum scheduling games, whereas it is drastic for generalized second price auctions.

Altruistic Hedonic Games

“…Exploring the properties of so-called considerate equilibria in resource selection games, Hoefer et al (2011) show that there exists a state that is stable with respect to selfish and considerate behavior at the same time. Anagnostopoulos, Becchetti, de Keijzer, and Schäfer (2013) study altruism and spite in strategic games. They consider directed weighted social networks where player i assigning a positive (negative) weight to player j means that i is altruistic (spiteful) towards j.…”

“…Rahn and Schäfer (2013) introduce yet another class of games, which they call social contribution games. They are motivated by the fact that altruistic behavior may actually render equilibria more inefficient (e.g., in congestion games) and may thus harm society as a whole (Anagnostopoulos et al, 2013). This is not the case for so-called valid utility games, though (Chen et al, 2014).…”

Additively Separable Hedonic Games with Social Context

“…Building on this model, Bilò et al [30] investigate social context games in which the underlying games are linear congestion games and Shapley cost sharing games, while the aggregation functions are min, max and sum. Moreover, Anagnostopoulos et al [31] study the effects of the altruistic behavior of players showing that the price of anarchy may increase as the players become more altruistic. They show that this increase is modest for congestion games and min-sum scheduling games, whereas it might be drastic for generalized second price auctions.…”

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

“…Exploring the properties of considerate equilibria in resource selection games, they show that there exists a state that is stable against selfish and considerate behavior at the same time. Anagnostopoulos et al (2013) study how the kind of altruistic behavior of players in social context games can make them in fact more inefficient, in the sense that the price of anarchy (relating the worst-case cost of a Nash equilibrium to the one of an optimal outcome) can thus be increased. Bilò et al (2013) apply the model of social context games by Ashlagi, Krysta, and Tennenholtz (2008) to linear congestion games and Shapley cost sharing games with the aggregation functions min, max, and sum (or average).…”

“…Rahn and Schäfer (2013) introduce another class of games, which they call social contribution games. They are motivated by the fact that, as we have seen above, altruistic behavior (i.e., taking other players' preferences or utilities into account when making a decision) may actually render equilibria more inefficient (e.g., in congestion games) and thus may harm society as a whole (Anagnostopoulos et al 2013). This is not the case for valid utility games, though, as Chen et al (2014) have shown that the inefficiency of equilibria remains unaltered under altruistic behavior in these games.…”