Stochastic Games: Existence of the Minmax

The Hebrew University of Jerusalem Stochastic Games: Existence of the Minmax

Absorbing Games with a Signalling Structure

The perfect monitoring assumption is replaced by a signalling structure that models, for each player, the information about the opponent’s previous action. The value of a stochastic game may not exist any more. For the class of absorbing games, we are able to show the existence of the maxmin and the minmax. The value does not exist if they are different.

Real Algebraic Tools in Stochastic Games

In game theory and in particular in the theory of stochastic games, we encounter systems of polynomial equalities and inequalities. We start with a few examples. The first example relates to the minmax value and optimal strategies of a two-person zero-sum game with finitely many strategies. Consider a twoperson zero-sum game represented by a k ×m matrix A = (aij), 1 ≤ i ≤ k and 1 ≤ j ≤ m. The n...

Pre-Bayesian Games

Work on modelling uncertainty in game theory and economics almost always uses Bayesian assumptions. On the other hand, work in computer science frequently uses non-Bayesian assumptions and appeal to forms of worst case analysis. In this talk we deal with Pre-Bayesian games, games with incomplete information but with no probabilistic assumptions about the environment. We first discuss safety-lev...

Explicit formulas for repeated games with absorbing states

Explicit formulas for the asymptotic value limλ→0 v(λ) and the asymptotic minmax limλ→0 w(λ) of finite λ-discounted absorbing games are provided. New simple proofs for the existence of the limits as λ goes zero are given. Similar characterizations for stationary Nash equilibrium payoffs are obtained. The results may be extended to absorbing games with compact action sets and jointly continuous ...