ON THE GENERIC FINITENESS OF EQUILIBRIUM OUTCOME DISTRIBUTIONS IN GAME FORMS

Article Abstract:

Consider nonempty finite pure strategy sets [S.sub.1], ..., [S.sub.n], let S = [S.sub.1] x ... x [S.sub.n], let [Omega] be a finite space of "outcomes," let [Delta]([Omega]) be the set of probability distributions on [Omega], and let [Theta]: S [right arrow] [Delta]([Omega]) be a function. We study the conjecture that for any utility in a generic set of n-tuples of utilities on [Omega[ there are finitely many distributions on [Omega] induced by the Nash equilibria of the game given by the induced utilities on S. We give a counterexample refuting the conjecture for n [is greater than or equal to] 3. Several special cases of the conjecture follow from well known theorems, and we provide some generalizations of these results. KEYWORDS: Generic finiteness, game forms, Nash equilibrium, semi-algebraic geometry.

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BEHAVIOR IN MULTI-UNIT DEMAND AUCTIONS: EXPERIMENTS WITH UNIFORM PRICE AND DYNAMIC VICKREY AUCTIONS

Article Abstract:

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop-out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions. KEYWORDS: Multi-unit demand auctions, uniform price auction, dynamic Vickrey auction, demand reduction, experiment.

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EFFICIENCY OF LARGE PRIVATE VALUE AUCTIONS

Article Abstract:

We consider discriminatory and uniform price auctions for multiple identical units of a good. Players have private values, possibly asymmetrically distributed and for multiple units. Our setting allows for aggregate uncertainty about demand and supply. In this setting, equlibria generally will be inefficient. Despite this, we show that such auctions become arbitrarily close to efficient if they are "large," and use this to derive an asymptotic characterization of revenue and bidding behavior. KEYWORDS: Auctions, efficiency, asymptotic efficiency, large auctions.

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