1. Introduction. Two person zero-sum differential games can be considered as control problems with two opposing controllers or players. One player seeks to maximize and one to minimize the pay-off function. The greatest pay-off that the maximizing player can force is termed the lower value of the game and similarly the least value which the minimizing player can force is called the upper value....

Game theory is a huge area of mathematical (and economical) research. We restrict ourselves mainly to two person zero-sum games, in which you make a decision and your opponent makes a decision (no cooperation allowed!), and your winnings equal your opponents loss. The main result is the so-called minimax theorem. Essentially, game theory is about playing against a (possibly) better player and e...

In this paper we study some relations between the optimal strategies, the characteristic roots and the characteristic vectors of a positive square matrix whose rows and columns correspond to the pure strategy spaces of players in a zero-sum two-person game. Further we study a property of the game values of positive matrices that commute. The results are extended to infinite games on the unit sq...

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...

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...

A dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay-o(s is equivalent to a primal–dual pair of such fuzzy linear programming problems. Further certain di6culties with similar studies reported in the literature are discussed. c © 2003 Elsevier B.V. All rights reserved.

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...