Two’s Company, Three’s an Equilibrium: Strategic Voting and Multicandidate Elections

In this paper, we characterize equilibria in games of electoral competition between three or more office-seeking candidates. Recognizing that electoral equilibrium involves both candidates’ and voters’ strategies, we first prove existence of pure strategy electoral equilibria when candidates seek to maximize their vote share. Accordingly, the main difficulty with electoral equilibria is multiplicity. We prove that, even after restricting attention to subgame perfect Nash equilibria in weakly undominated strategies, the set of electoral equilibria is very large. We provide several characterizations of candidates’ equilibrium platforms, including a set of conditions under which equilibrium platforms are located in the minmax set. We also examine welfare implications of the results, connections between the noncooperative equilibria, the core, and the uncovered set. Finally, we show that the paper’s results do not depend upon whether any or all of the candidates are maximizing their vote-share, plurality, or their probability of victory.