Conferences at Department of Economics, University of Toronto, Canadian Economic Theory Conference 2016

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Repeated Competing Mechanisms

Seungjin Han*, Sambuddha Ghosh

Date: 2016-05-08 10:45 am – 11:15 am
Last modified: 2016-04-28

Abstract


This paper studies the repeated game where multiple principals compete to offer short-term mechanisms to multiple agents repeatedly over time. A mechanism is sufficiently general to make a principal’s short-term action con- tingent on agents’ messages that may reflect changes in the market or agents’ payoff types. In the case with no private information on agents’ types, there is no distinction between the repeated and one-shot game in terms of set of equilibrium allocations: A principal’s lower-bound of equilibrium payoff is expressed as his minmax value over random action space in both games. In the case with private information on agents’ types, there are significant differ- ences. In the repeated game, a weaker notion of incentive compatibility can be applied and the deviating principal cannot do any better with offering an arbitrary mechanism off the path following his deviation than he does with offering a single action. In contrast to the one-shot game, this allows us to express a principal’s lower-bound of equilibrium payoff in the repeated game in terms of model primitives: It is equal to his maxmin value over his action space and the other principals’ incentive compatible direct mechanisms con- ditional on the principal’s action. This lower-bound is lower than that in the one-shot setting. The weaker notion of incentive compatibility can be also ap- plied to the equilibrium allocations. Combining it with the lower low-bound imply that the repeated game supports more allocations in equilibrium. 


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