We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. will establish the value function under total variation, setwise, and weak convergence structures. Our analysis reveals that for bounded is continuous variation structures in both zero-sum games team problems. Continuity ...

We introduce generous, even-matched, and greedy strategies as concepts for analyzing games. A two person prisoner's dilemma game is described by the four outcomes (C,D), (C,C), (D,C), and (D,D). In a generous strategy the proportion of (C,D) is larger than that of (D,C), i.e. the probability of facing a defecting agent is larger than the probability of defecting. An even-matched strategy has th...

In 1967 Aumann and Maschler presented their celebrated model for games with incomplete information, see [1] and references therein. The game they consider consists in a set of, say I, standard discrete time two person zero-sum games. At the beginning one of these zero-sum games is picked at random according to a probability p. The information which game was picked is transmitted to Player 1 onl...

Formalization of a 2 Person Zero-Sum Game 1. There are two players, P1 and P2. 2. P1 has a set A = {a1, a2, . . . , am} of m pure strategies (or actions). 3. P2 has a set B = {b1, b2, . . . , bn} of n pure strategies (or actions). 4. Each player has a utility for each (ai, bj) pair of actions. The utility for P1 is denoted U1(ai, bj) and the utility for P2 is denoted U2(ai, bj). Since this is a...

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P . We show that the upper Snell envelope Z of the reward process Y is a supermarti...