The risk-neutral equilibrium bidding strategy for first-price auctions with independent private values is justified without assuming a well-defined Bayesian game. Bidders, aware of their own value, assume the private values to be linearly related. The latter, however, are independent and...

A social game is a generalization of a strategic-form game, in which not only the payoff of each player depends upon the strategies chosen by their opponents, but also their set of admissible strategies. Debreu (1952) proves the existence of a Nash equilibrium in social games with continuous...