Distribution-Free Equilibrium in Search Contests

We study a contest in which $N$ players sequentially draw from a distribution as many times as they want at a fixed cost per draw, with no recall, and the highest accepted value wins a prize. In the unique symmetric equilibrium, the acceptance probability, expected search cost, and players' payoffs do not depend on the underlying distribution. Total search expenditure equals the prize (full rent dissipation). These distribution-free equilibrium properties extend to multiple prizes and to hierarchical competition among designers. The efficient prize that aligns competitive incentives with the social optimum is distribution-dependent: heavy-tailed distributions require much larger prizes. With finite number of draws, adding competitors can raise the quality threshold when search costs are low, reversing the discouragement of the unlimited-draw case. A planner choosing both the prize and the field size always prefers the minimum field ($N=2$) with unlimited draws, but heavy-tailed distributions and finitely many draws favor larger fields, as breadth of parallel exploration compensates for limited depth of individual search.