The Generalized War of Attrition

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Abstract
The authors model a war of attrition with N+K firms competing for N prizes. In a 'natural oligopoly' context, the K - 1 lowest-value firms drop out instantaneously, even though each firm's value is private information to itself. In a 'standard setting' context, in which every competitor suffers losses until a standard is chosen, even after giving up on its own preferred alternative, each firm's exit time is independent both of K and of other players' actions. The authors' results explain how long it takes to form a winning coalition in politics. Solving the model is facilitated by the revenue equivalence theorem.

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