The evolution of conventions in minimum effort games

• We study the equilibrium selection problem in a more general minimum effort game.
• Conditions for a unique stochastically stable equilibrium (SSE) to exist are studied.
• We show that with two players the SSE is also the only maximum potential of the game.
• For linear effort disutility the efficiency of SSE depends on the distributional rule.
• For nonlinear effort disutility the SSE is inefficient; distribution does not matter.

The literature on minimum effort game has been concerned with a symmetric game with linear payoff functions. The main aim of the present paper is to study the coordination problem arising in a not necessarily symmetric minimum effort game with two players. The sources of asymmetry can be twofold: the productivity of effort and the distribution of the join output. To select among the Pareto ranked equilibria we use the stochastic stability criterion. We show that, for any configuration parameters, the set of stochastically stable equilibria coincides with the set of potential maximizers. We also show that when the disutility of effort is linear, the Pareto dominant equilibrium is stochastically stable provided that the distributive parameter belongs to a well defined range. When the disutility of effort is nonlinear no distributive arguments can be used to successfully affect the selection process. Lastly we prove that the connection between stochastic stability and maximum potential can fail when more than two agents are considered.