ZERO-SUM GAMES WITH STOPPING TIMES AND VARIATIONAL INEQUALITIES

Two Player Non Zero-sum Stopping Games in Discrete Time

We prove that every two player non zero-sum stopping game in discrete time admits an -equilibrium in randomized strategies, for every > 0. We use a stochastic variation of Ramsey Theorem, which enables us to reduce the problem to that of studying properties of -equilibria in a simple class of stochastic games with finite state space.

A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

Zero-sum games with charges

We consider two-player zero-sum games with countably infinite action spaces and bounded payoff functions. The players’ strategies are finitely additive probability measures, called charges. Since a strategy profile does not always induce a unique expected payoff, we distinguish two extreme attitudes of players. A player is viewed as pessimistic if he always evaluates the range of possible expec...

Variational inequalities in Hilbert spaces with measures and optimal stopping

We study the existence theory for parabolic variational inequalities in weighted L spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L setting allows us to cover some singular cases...

Perturbed zero - sum games with appli ations