Computing equilibria using interval constraints

Abstract

Finding NASH equilibria is a hard computational problem which is central to game theory and whose applications range from decision-making to the analysis of multi-agent systems. Despite considerable recent interest and significant recent improvements, the problem remains essentially open in the case of n-person games. We investigate the use of interval-based constraint solving techniques to compute equilibria. We report on experiments made using several encodings of randomly-generated games into continuous CSP, and draw conclusions regarding both the scalability of interval methods for game-theoretic applications and the impact of the symbolic representation of polynomials and of the choice of the propagation technique on the speed of resolution. © Springer-Verlag Berlin Heidelberg 2005.