Algorithms for stochastic games and polynomial system solving

12^th April 2016, 13:00 Ashton Lecture Theater
Dr. Elias Tsigaridas
UPMC - LIP6
projet POLSYS
Boite courrier 169
4 place Jussieu
75252 PARIS CEDEX 05
France

Abstract

Shapley's discounted stochastic games and Everett's recursive games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We present an exact algorithm for solving such games based on separation bounds from real algebraic geometry. When the number of positions of the game is constant, the algorithm runs in polynomial time and is the first with this property. If time permits, we will also present lower bounds on the algebraic degree of the values of stochastic games, induced from the irreducibility of polynomials that have coefficients that depend on the combinatorial parameters of the games, based on a generalization of Eisenstein criterion.