In sequential decision making, heuristic search algorithms allow exploiting both the initial situation and an admissible to efficiently for optimal solution, often planning purposes. Such exist problems with uncertain dynamics, partial observability, multiple criteria, or collaborating agents. this article, we look at two-player zero-sum stochastic games (zsSGs) a discounted criterion, in view ...

Many security and other real-world situations are dynamic in nature can be modelled as strictly competitive (or zero-sum) games. In these domains, agents perform actions to affect the environment receive observations -- possibly imperfect about situation effects of opponent's actions. Moreover, there is no limitation on total number an agent that is, fixed horizon. These settings partially obse...

Until this day, no counter example was found. Furthermore, we have seen that a positive answer was given for several special classes, including recursive games (Everett, 1957), zero-sum games (Mertens and Neyman, 1981), two-player absorbing games (Vrieze and Thuijsman, 1989) and two-player non zero-sum games (Vieille, 1997b). For n-player games, existence of stationary equilibrium profiles was ...

In this lecture we will discuss 2-player zero sum games. Such games are completely competitive , where whatever one player wins, the other must lose. Examples of such games include chess, checkers, backgammon, etc. We will show that in such games: • An equilibrium always exists; • All equilibrium points yield the same payoff for all players; • The set of equilibrium points is actually the carte...