Since seminal works by Neumann-Morgenstern(J.VonNeunann, 1994) and Nash(J.F.Nash., 1950 & J.F.Nash., 1951), Game theory has played an important role in the fields of decision making theory such as economics, management, and operations research, etc. When we apply the game theory to model some practical problems which we encounter in real situations, we have to know the values of payoffs exactly...

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...

In 1951, Dantzig [3] showed the equivalence of linear programming and two-person zero-sum games. However, in the description of his reduction from linear programming to zero-sum games, he noted that there was one case in which his reduction does not work. This also led to incomplete proofs of the relationship between the Minmax Theorem of game theory and the Strong Duality Theorem of linear pro...

This paper is concerned with two-person non-zero-sum game versions of the secretary problem. A remarkable feature of our models compared with previous ones is that Nash equilibrium strategies are different for two players, i.e. one player should behave more hastily, and the other less hastily, than in the secretary problem.

The paper studies the open-loop saddle point and lower upper values, as well their relationship for two-person zero-sum stochastic linear-quadratic (LQ) differential games with...

We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds controls. assume that Player 1 uses piecewise-continuous controls, while 2 impulse For this games, we seek to derive conditions for the existence feedback Nash equilibrium strategies players. More specifically, provide verification theorem identifying such st...