Equilibrium Social Hierarchies: A Non-Cooperative Ordinal Status Game

We analyze a game in strategic form, where each player's payoff depends on his action and his social status, which is given by his rank in the actions distribution. Our focus is on the relation between the degree of heterogeneity among status-seeking players and the distribution of their Nash equilibrium actions. We find that if among players intrinsic concerns are sufficiently important relative to status concerns, individual equilibrium actions diverge, but if status concerns are relatively important, individual equilibrium actions are the same. Another key result of the analysis is that, in contrast to what is usually claimed, status seeking need not always be socially inefficient. If players are sufficiently heterogeneous, there exists a Nash equilibrium that is unique, separating, and Pareto efficient.