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An auction allocates goods using submitted messages and a specified payment rule. Private-value auctions model each bidder's valuation as its own private information. Equilibrium bids depend on the allocation and payment rules, not only on valuations.

A Bayesian game gives players private information about their types, a probability model for that information, and strategies depending on the player's own type. A private-value auction with uncertain other valuations is a Bayesian game.