Participation games and Bernstein polynomials

Jorge Peña (IAST)

March 15, 2018, 11:00–12:15


Room MS 001

MAD-Stat. Seminar


Economists, biologists, and social scientists have studied several kinds of participation games where each player choses whether or not to participate in a given activity and payoffs depend on the own decision and the number of players who participate. The symmetric mixed strategy equilibria of such games are given by equations that involve expectations of functions of binomial variables giving rise to Bernstein polynomials. Such polynomials are endowed with interesting shape preserving properties, well known in the field of computer aided design but often ignored in game theory. Here, I review previous and current work demonstrating how the use of these properties allows us to easily identify the number of symmetric mixed equilibria and to sign their group size effect for a fairly large class of participation games. I illustrate this framework with several applications from the economic and political science literature. Our results, based on Bernstein polynomials, provide formal proofs for previously conjectured results in a straightforward way.