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Stochastic Equivalence in Sequential Auctions with New Buyers

Said, Maher (2008): Stochastic Equivalence in Sequential Auctions with New Buyers.

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Abstract

We examine markets in which multiple buyers with single-unit demand are faced with an infinite sequence of potential transactions that occur at random times. Moreover, the set and number of buyers are not fixed throughout this sequence; instead, additional buyers may arrive probabilistically on the market in each period. Buyer valuations are independently distributed, and objects are stochastically equivalent. We solve for the expected payoffs of buyers when trade occurs via sequential second-price auctions, and examine the manner in which the option value of future auctions, and hence bidding behavior, varies with both current market conditions and anticipated future dynamics. In addition, we consider the case when buyer valuations are persistent in the sense that distributions are chosen according to a Markov process, and provide a generalization of our result to this setting.

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