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.
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 use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large dataset of internet auctions. The theory agrees with the data with striking accuracy for small population size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different phases, one in which adaptation is feasible and one in which it is not . Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.
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use a grand canonical approach to
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the game
strategies. We then study the properties of the solution
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N and study its properties, which are then compared
the mean number of players, and compare them
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empirical collective strategy reproduces the theoretical equilibrium
theory agrees with the data
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population size
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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
a qualitatively different distribution is observed. We interpret this result as the emergence of two different phases, one in which adaptation is feasible and one in which it is not