Ex ante efficient, ex post individually rational trade
Consider a model of bilateral trade in which each trader's valuation is private information. The mechanism for establishing the terms of trade will determine the percentage of available gains from trade that can be realized on average by the degree to which it encourages or discourages strategic bargaining. A mechanism can be thought of as having two components: a trading rule and a payment rule. The first processes the traders' valuations reports, which need not be truthful, and determines whether or not trade should occur. The payment rule, again using the reported valuations, determines whether or not any money changes hands. \textit{R. B. Myerson} and \textit{M. A. Satterthwaite} [J. Econ. Theory 29, 265-281 (1983; Zbl 0523.90099)] characterize the set of all incentive compatible mechanisms that maximize the expected gains from trade while guaranteeing each trader a non-negative return conditional on his valuation (interim individual rationality). Call such mechanisms incentive efficient. They show that the requirement of interim individual rationality leads to a loss in trading efficiency. This is in contrast to the work of \textit{C. D'Aspremont} and \textit{L.-A. Gérard-Varet} [J. Publ. Econ. 11, 25-45 (1979)]. They construct an incentive compatible mechanism that realizes all available gains from trade while guaranteeing each trader a non-negative (unconditional) expected return. For any given set of beliefs about each trader's valuation, many incentive efficient mechanisms exist because the constraints on the set of possible payment rules define a system of integrodifferential equations that admit many solutions. All previously reported solutions could be considered unsatisfactory because, on a set of valuations of positive measure, they either require the buyer to pay the seller when there is no associated trade or when trade does occur, they specify a money transfer that exceeds the buyer's valuation or is less than the seller's valuation. This paper derives weak sufficient conditions for a solution to the payment rule constraint system to exist that exhibits neither of these properties. Mechanisms with such rules guarantee each trader a non-negative return from trade conditional on both traders' valuations and are called ex post individually rational. As the proof is constructive, an explicit solution is offered. Thus, this paper demonstrates that it is generally possible to require trading mechanisms to satisfy this stronger individual rationality property without any additional loss of trading efficiency. Finally, \textit{St. A. Matthews} and \textit{A. Postlewaite} [J. Econ. Theory 48, 238-263 (1989; Zbl 0673.90102)] conjecture that with pre-play communication an equilibrium of a sealed- bid double auction exists that achieves the second-best level of trading efficiency defined by Myerson and Satterthwaite. Our results confirm this conjecture for a large open class of trader beliefs.
scientific article; zbMATH DE number 4204082
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