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In lowest unique bid auctions, $N$ players bid for an item. The winner iswhoever places the \emph{lowest} bid, provided that it is also unique. We use agrand canonical approach to derive an analytical expression for the equilibriumdistribution of strategies. We then study the properties of the solution as afunction of the mean number of players, and compare them with a large datasetof internet auctions. The theory agrees with the data with striking accuracyfor small population size $N$, while for larger $N$ a qualitatively differentdistribution is observed. We interpret this result as the emergence of twodifferent regimes, one in which adaptation is feasible and one in which it isnot. Our results question the actual possibility of a large population to adaptand find the optimal strategy when participating in a collective game.

Equilibrium strategy and population-size effects in lowest unique bid auctions