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Generalizing mechanism design theory to a case where agents' types are adjustable

Wu, Haoyang (2018): Generalizing mechanism design theory to a case where agents' types are adjustable.

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In 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. Since the designer does not know each agent's private type, what she can do is to construct a mechanism and choose an outcome after observing a profile of agents' strategies. There is a dilemma in the sense that even if the designer is not satisfied with some outcome, she has to obey the mechanism designed by herself and announce this outcome. In this paper, we generalize the mechanism design theory to a case where the designer can take some action to actively adjust agents' private types, and yield a more favorite outcome. After defining a series of notions such as adjustable types, optimal adjustment cost and profitably Bayesian implementability, we propose that the traditional notion of Bayesian incentive compatibility does not hold in this generalized case. Finally, we construct a model to illustrate that the auctioneer can obtain an expected profit greater than what she obtains in the traditional optimal auction.

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