Srihari Govindan | University of Rochester

::;Ng has a general type space  n, and there's a prior p on   = QN n=1  n that is absolutely continuous with respect to the product of its marginals. The action space An of player n is compact Hausdor. The outcome space, denoted (Z), is the set of probability distributions over a nite set Z. The outcome function is given by  : A ! (Z), where A = QN n=1 An. Transfers are denoted by tn and payos by un :    Z  R ! R, so un(!; z; tn) is the payo to n when the type prole is !, the outcome is z and the payment he makes is tn. We assume that the game is \mildly discontinuous" in the sense that  is continuous almost everywhere. The model subsumes standard auction models. We provide sucient conditions for the existence of Nash equilibria in mixed strategies as well as in pure strategies, and also "-Nash equilibria in these games and explore the implications of these results for auctions.

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