Symbolic Computation of Sequential Equilibria

Abstract

The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a sequential equilibrium if it satisfies the properties of sequential rationality and consistency. Our main result is that both properties together can be written as a single finite system of polynomial equations and inequalities. The solutions to this system are exactly the sequential equilibria of the game. We construct this system explicitly and describe an implementation that solves it using cylindrical algebraic decomposition. To write consistency as a finite system of equations, we need to compute the extreme directions of a set of polyhedral cones. We propose a modified version of the double description method, optimized for this specific purpose. To the best of our knowledge, our implementation is the first to symbolically solve general finite imperfect information games for sequential equilibria.