On discrete preferences and coordination

An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and the decisions of her neighbors. A basic question that has remained largely open is to consider games where the players' strategies come from a fixed, discrete set, and where players may have different preferences among the possible strategies. We develop a set of techniques for analyzing this class of games, which we refer to as discrete preference games. We parametrize the games by the relative extent to which a player takes into account the effect of her preferred strategy and the effect of her neighbors' strategies, allowing us to interpolate between network coordination games and unilateral decision-making. We focus on the efficiency of the best Nash equilibrium and provide conditions on when the optimal solution is also a Nash equilibrium.