Nicholas Vieille

Professor Vieille is honored for three papers:

• Two-Player Stochastic Games I: A Reduction, Israel Journal of Mathematics, 119, pp. 55-91, 2000.
• Two-Player Stochastic Games II: The Case of Recursive Games, Israel Journal of Mathematics, 119, pp. 93-126, 2000.
• Small Perturbations and Stochastic Games, Israel Journal of Mathematics, 119, pp. 127-142, 2000.

They answer, fifty years after the question was put, whether every undiscounted two -person stochastic game has an equilibrium. Stochastic games, which generalize Markov decision processes, were introduced in 1953. The first equilibrium existence result for a non-trivial instance was published in 1968. Fifteen years later, existence of equilibrium payoffs in two-person zero-sum undiscounted stochastic games was established. The more general question remained open until Vieille's breakthrough proving the existence of equilibrium payoffs in the non-zero-sum case. The proof is both deep and innovative. The mathematical tools devised by Vieille are applicable to more general cases and are currently employed by researchers in the field.