
Journal of Convex Analysis 30 (2023), No. 2, 481498 Copyright Heldermann Verlag 2023 Existence and Statistical Estimation of Equilibria in Stochastic Electoral Competitions Adib Bagh Depts. of Mathematics and Economics, University of Kentucky, Lexington, U.S.A. adib.bagh@uky.edu We establish the existence of a Nash equilibrium in a class of stochastic games representing electoral competitions between two candidates facing a continuum of voters. The underlying uncertainty in such games is due to the fact that candidates are uncertain about the fraction of the voters that will actually vote for them on election day. The payoff functions of the candidates are neither continuous nor concave. Therefore, we transform a game in this class into a new game with nicer geometric and continuity properties. We establish the existence of an equilibrium for the new game using a standard fixed point argument, and we finally show that an equilibrium of the new games is also an equilibrium of the original game. We further show the equilibria we found can be approximated statistically using nonparametric maximum likelihood estimators of the distribution of the random variable representing the uncertainty in the game. Keywords: Stochastic voting models, Nash Equilibrium, logconcave random variables, nonparametric maximum likelihood estimators. MSC: 91A80, 90C15, 62F12. [ Fulltextpdf (159 KB)] for subscribers only. 