Heterogeneous network games: Conflicting preferences

Abstract

Abstract:In many economic situations, a player pursues coordination or anti-coordination with her neighbors on a network, but she also has intrinsic preferences among the available options. We here introduce a model which allows to analyze this issue by means of a simple framework in which players endowed with an idiosyncratic identity interact on a social network through strategic complements or substitutes. We classify the possible types of Nash equilibria under complete information, finding two thresholds for switching action that relate to the two-player setup of the games. This structure of equilibria is considerably reduced when turning to incomplete information, in a setup in which players only know the distribution of the number of neighbors of the network. For high degrees of heterogeneity in the population the equilibria is such that every player can choose her preferred action, whereas if one of the identities is in the minority frustration ensues.

Equilibria, information and frustration in heterogeneous network games with conflicting preferences

“…We then study in Sec. III the dynamically relevant equilibria and compare them with the ones found in [31,32] with an analytical, static approach. Subsequently, we also extend the study to the case of a scale-free network and Proportion Imitation, comparing the differences when the same games are played in the absence of individual preferences.…”

“…Let us call χ i the number of agent i's neighbors who choose action 1, so the number of neighbors that choose action 0 is k i − χ i . As described in [31], from the purely static, theoretical viewpoint in economics, we have two thresholds to compare with χ i in order to permit to agent i to decide which action to take:…”

“…We here study this issue in a very broad range of socially relevant scenarios, by using the model introduced by Hernández et al [31]. This is a generalization of earlier work [27] where two entire classes of games were studied, namely coordination games and social dilemmas (more precisely, strategic complements and strategic substitutes) in random networks.…”

“…This is a generalization of earlier work [27] where two entire classes of games were studied, namely coordination games and social dilemmas (more precisely, strategic complements and strategic substitutes) in random networks. In [31], the problem of diversity in preferences was analyzed by considering that there are two different types of players in the population, and that each type prefers (because the corresponding payoff is larger) one of the two available actions. Therefore, coordination and/or cooperation becomes more difficult, in so far that agents have incentives to choose a specific action that yields more benefit to them irrespective of the choices of those with whom they interact.…”

The Shapley value for the network game with pairwise interactions

“…Finding equilibrium in online gaming as an example of Designer-Adversary game was described in [4]. Cooperation in the network games and model of interaction between coalitions is considered in [3]. Pairwise interaction was exposed on the example of dissemination of information and misinformation in social networks, in [8].…”