Implementation in Bayesian equilibrium: the multiple equilibrium problem in mechanism design

Abstract

INTRODUCTION Implementation theory links together social choice theory and game theory. At a less abstract level, its application provides an approach to welfare economics based on individual incentives. The underlying motivation for implementation theory is most easily seen from the point of view of a relatively uninformed planner who wishes to optimize a social welfare function that depends on environmental parameters about which relevant information is scattered around in the economy. Thus, the planner wishes to both collect as much of this relevent information as possible, and, with this information, make a social decision (e.g., an allocation of resources). This is the classic problem identified by Hurwicz (1972). In the twenty years since, we find numerous research agendas falling into the general category of implementation problems: the study of planning procedures, contracts, optimal regulation and taxation, agency relationships, agendas and commitee decision-making, comparative electoral systems, non-cooperative foundations of general equilibrium theory, and even much of the recent theoretical work in accounting and the economics of law. The dilemma such a planner faces is that the individuals from whom the information must be collected will not necessarily want to share their information, or worse, they may wish to misrepresent their information. Moreover, exactly how they choose to conceal and misrepresent their information (what we will call their deception decision ) depends upon three things. First and foremost, it depends on expectations of how the planner intends to put to use the information that is being collected. Second, it depends upon their expectations about the deception decisions of the other agents. Third, it depends on their information, so it is convenient to think of a deception decision as a plan of what to reveal as a function of information.

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