Discontinuous and Continuous Stochastic Choice and Coordination in the Lab

Abstract

Coordination games have multiple equilibria under complete information. However, recent theoretical advances show that if players are uncertain but can acquire information about a payoff-relevant state of the world, the number of equilibria depends on whether they can implement strategies (stochastic choice rules) discontinuous in the state. We experimentally test these results in a two-player investment game. Through a minimal visual variation in the design (our treatment) we prompt participants to play strategies whereby their probability to invest is either continuous or discontinuous in the payoff-relevant state. When participants use continuous strategies, average behavior is consistent with play in the risk-dominant equilibrium, the unique theoretical prediction. When they use discontinuous strategies—in¬¬ which case there are multiple equilibria—average behavior is closer to the payoff-dominant equilibrium strategy. Additionally, we extend the theory to heterogeneous populations: the set of equilibria monotonically decreases in the proportion of players who use continuous strategies.