Theoretical Economics 2 (2007), 299–354

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### Efficiency in repeated trade with hidden valuations

*Susan Athey, David A. Miller*

#### Abstract

We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents with hidden valuations (i.i.d. over time), restricting attention to equilibria that satisfy ex post incentive constraints in each period. With ex ante budget balance, efficient trade can be supported in each period if the discount factor is at least one half. In contrast, when the budget must balance ex post, efficiency is not attainable, and furthermore for a wide range of probability distributions over their valuations, the traders can do no better than employing a posted price mechanism in each period. Between these extremes, we consider a "bank'' that allows the traders to accumulate budget imbalances over time, but only within a bounded range. We construct non-stationary equilibria that allow traders to receive payoffs that approach efficiency as their discount factor approaches one, while the bank earns exactly zero expected profits. For some probability distributions there exist equilibria that yield exactly efficient payoffs for the players and zero profits for the bank, but such equilibria require high discount factors.

Keywords: Repeated trade, Myerson-Satterthwaite Theorem, repeated games, private information, dynamic mechanism design, ex post incentive compatibility, budget balance

JEL classification: C72, C73, D82, L14

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