A revision game of experimentation on a common threshold

Abstract

A revision game of experimentation is examined in which players search for an unknown threshold. Each player encounters individual random opportunities to revise her own action. Lower action saves flow cost, but the player whose action falls below the threshold suffers a costly breakdown and exits the game. The set of symmetric pure-strategy Markov equilibria has a simple characterization. The difference between these equilibria vanishes as the revision opportunity becomes infinitely frequent. In all such equilibria, players revise actions gradually over time and, absent breakdowns, settle asymptotically. The asymptotic level of actions decreases with the patience of the players, and the speed of decline in actions decreases with the number of players. In equilibrium, the endogenous arrival rate of breakdown is decreasing over time. The model extends to incorporate collateral damage from breakdowns, where two competing externalities jointly shape the dynamics.