Strategic Exploration: Preemption and Prioritization

Abstract

This paper provides a model of strategic exploration in which two competing players simultaneously explore a set of alternatives over time to study search dynamics, payoff divisions, and distributions of discovery time. The strategic tension is between preemption, i.e., the incentive to covertly explore alternatives that the opponent will explore in future, and prioritization, i.e., the incentive to explore alternatives with the highest success probabilities. We show that players randomize over the same set of alternatives that expands over time, duplicating each other’s explorations from start to finish. When players are symmetric in their speed of exploration, equilibrium strategies are greedy. In the asymmetric case, the weak player’s strategy is greedy, but the strong player randomizes over alternatives with different posteriors and captures a share of payoff disproportionately larger than his share of exploration capacity. The weak player conducts extensive instead of intensive exploration, i.e., he covers as many alternatives as the strong player does but never explores any alternative with cumulative probability one. The overall discovery time decreases in asymmetry in the first-order stochastic dominance sense.