On Monday, 7-May-2012, we had a one-day conference at Tel Aviv University, and awarded the 2012 Michael Maschler prize for an outstanding research student. The prize committee, comprised of three professors from different institutions, wrote:
Stochastic games have been introduced and studied by Lloyd Shapley in 1953. Since then they have proved to be challenging to game theorists as well as useful in a wide range of applications in economics, evolutionary biology, and computer science.
Yehuda Levy has recently succeeded in settling a long-standing open problem concerning the existence of equilibria in stochastic games. This problem has attracted over the last four decades the attention of many scholars and was studied by the most capable researchers in the field. Specifically, the question was whether every discounted stochastic game has a stationary equilibrium. Levy answers this question in the negative. His work on this problem goes well beyond just solving it. He constructs a discounted stochastic game without a measurable stationary equilibrium, which, moreover, has neither a stationary correlated equilibrium, nor a stationary approximate equilibrium. Levy also proves that a stochastic game with a continuum of states and with transition probabilities absolutely continuous with respect to some fixed measure, need not have a stationary equilibrium. This result contrasts with the known existence of stationary approximate equilibria in this case.
In his work Yehuda Levy has made one of the most important advances in stochastic games, and more broadly in game theory, in the past decade. His work will be a classic in game theory.
The winner, Yehuda (John) Levy, was a little nervous before, while, and after shaking hands, receiving the nice flowers sent by the Center for Rationality, and getting the award. I hope to have enough time this summer to fully understand his construction and report it here.
From left: David Schmeidler, Eilon Solan, Yehuda (John) Levy, Hana Maschler, Yisrael Aumann