A Solution Concept for Majority Rule in Dynamic Settings∗

We define and explore the notion of a Dynamic Condorcet Winner (DCW), which extends the notion of a Condorcet winner to dynamic settings. We show that, for every DCW, every member of a large class of dynamic majoritarian games has an equivalent equilibrium, and that other equilibria are not similarly portable across this class of games. Existence of DCWs is guaranteed when members of the community are sufficiently patient. We characterize sustainable and unsustainable outcomes, study the effects of changes in the discount factor, investigate efficiency properties, and explore the potential for achieving renegotiation-proof outcomes. We apply this solution concept to a standard one-dimensional choice problem wherein agents have single-peaked preferences, as well as to one involving the division of a fixed aggregate payoff. ∗We would like to thank Avinash Dixit, Roger Myerson, Antonio Rangel, members of the Public Economics Group at Stanford University, participants at various seminar presentations, and several anonymous referees for helpful comments. This paper was prepared in part while Bernheim was a Fellow at the Center for Advanced Study in the Behavioral Sciences (CASBS), where he was supported in part by funds from the William and Flora Hewlett Foundation (Grant #2000-5633), and while Slavov was a graduate student at Stanford University, where she was supported by an NSF Graduate Research Fellowship. Bernheim gratefully acknowledges financial support from the NSF (grants SES-0137129 and SES-0452300).