Rational and actual behavior in lowest unique bid auctions

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We derive an analytical expression for the equilibrium distribution of the game as a function of N and study its properties, which are then compared with a large dataset of internet auctions. The empirical collective strategy reproduces the theoretical equilibrium with striking accuracy for small N, while for larger N the quality of the fit deteriorates. As a consequence, the same game exhibits lottery-like and game-of-skill features, depending on the collective size of the bidding pool. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.