A two person zero sum matrix game with fuzzy goals and fuzzy payoffs is considered and its solution is conceptualized using a suitable defuzzification function. Also, it is proved that such a game is equivalent to a primal-dual pair of certain fuzzy linear programming problems in which both goals as well as parameters are fuzzy.

We have studied two person stochastic di erential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero sum case we have proved the existence of a Nash equilibrium.

In this section we study games with only two players. We also restrict attention to the case where the interests of the players are completely antagonistic: at the end of the game, one player gains some amount, while the other loses the same amount. These games are called “two person zero sum games”. While in most economics situations the interests of the players are neither in strong conflict ...

Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528–1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guaran...

Lines of Action (LOA) is a two-person zero-sum game with perfect information; it is a chess-like game with a connection-based goal. In this note the 6 × 6 variant of LOA is weakly solved. A Proof-Number search method, PN, is used to compute that the game is a win for the first player (Black). Based on the results of solving the boards up to 6× 6, an optimistic time frame is given for solving 7×...

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also inves...