Hard evidence and mechanism design
In its standard “public choice” form, the mechanism-design framework abstracts from institutional and technological constraints beyond those that the modeler can represent in the definition of states, outcomes, and preferences. This abstraction can create a useful simplification. However, there are real constraints that we are interested in studying but that cannot be incorporated into the standard framework. For example, in many settings, parties can present hard evidence. The key features of hard evidence are that (a) whether to present evidence is an inalienable decision, and (b) the existence of evidence depends on the state. We show how hard evidence can be incorporated into the mechanism-design framework. This is particularly interesting in two player settings, which much of the recent contract theory literature has focused on, because, in general, more outcome functions can be implemented than can be with standard Nash implementation. A key objective is to address the meaning and validity of the revelation principle in the context of hard evidence. We address the degree to which the parties' behavior in a mechanism can be interpreted as abstract “declarations of the state.” We provide a link between real evidence and abstract declarations, which clarifies when the abstract-declaration environment, which was first studied in Green and Laffont's (1986) “limited verifiability” analysis, has an intuitive interpretation. We find that the condition of evidentiary normality---under which, for each party, there is a one-to-one mapping between states and report/evidence pairs that holds across all implementation exercises---justifies studying the abstract-declaration model. However, without evidentiary normality, it is not appropriate to focus on static mechanisms. We show that, regardless of whether evidentiary normality holds, any implementable outcome function can be implemented with a two-stage dynamic mechanism, in which players simultaneously send messages and
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