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Profitable Bayesian implementation in one-shot mechanism settings

Wu, Haoyang (2019): Profitable Bayesian implementation in one-shot mechanism settings.

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In the mechanism design theory, a designer would like to implement a desired social choice function which specifies her favorite outcome for each possible profile of all agents' types. In a standard one-shot mechanism, the agents interact only once and the designer has no way to adjust agents' types. Hence, the designer may be in a dilemma in the sense that even if she is not satisfied with some outcome with low profit, she has to announce it because she must obey the mechanism designed by herself. In this paper, we investigate a case where the designer can induce each agent to adjust his type in a one-shot mechanism. After defining a series of notions such as adjusted types, optimal adjustment cost and profitable Bayesian implementability, we propose that the revelation principle does not hold in this generalized case. Finally, we construct an example to show that the designer can obtain an expected profit greater than the maximum profit that she can obtain in the traditional optimal auction.

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