Strategic Experimentation on a Common Threshold

Abstract

A revision game of experimentation is examined in which players search for an unknown threshold. Players encounter individual random opportunities to revise actions. Lower actions save 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 is characterized. The difference between these equilibria vanishes as the revision opportunity becomes in finitely frequent. In all such equilibria players revise actions gradually over time and settle asymptotically at a higher-than-minimum level, absent breakdowns. The actions settle at higher levels with less patient players, and the decline is slower with more players. The on-path 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.