Players in a search contest draw scores from an unknown distribution, one draw at a time, at a cost per draw. No recall — you use your last draw or keep searching. The highest score wins a prize. The question: when should you stop searching and accept your current score?
Erkurt and Ozdenoren prove that in the unique symmetric equilibrium, the acceptance probability depends only on the number of players, the cost, and the prize. Not on the distribution. Whether scores are drawn from a uniform, normal, exponential, or any other distribution, the optimal stopping rule is the same. The equilibrium is distribution-free.
This is not a robustness result — it is not that the equilibrium is approximately the same across distributions. It is exactly the same. The acceptance threshold adjusts to the distribution, but the probability of accepting at each draw is invariant. Furthermore, total expenditure across all players equals the prize, regardless of the distribution. The contest extracts full surplus as a structural property, not as a consequence of any particular distributional assumption.
The through-claim is about what determines strategic behavior. In most contest models, the distribution matters — the shape of the payoff function, the tail behavior, the variance all influence how much players invest. Here, the distribution drops out entirely. The competitive structure — how many players, what it costs to search, what you win — contains all the information needed to determine behavior. The randomness of the scores creates the uncertainty that drives the contest, but the specific character of that randomness is irrelevant to the equilibrium. The game absorbs the distribution.