The world oil market is modelled as a two-person non-zero-sum game in normal form with each player having a continuum of strategies. The two players are the oil importing nations (OPIC) and the oil exporting nations (OPEC). The game is solved in the noncooperative sense using the equilibrium point solution concept due to Nash. The Nash equilibrium point solution yields an analytic expression fo...

In this paper we study a two person zero sum stochastic differential game in weak formulation. Unlike the standard literature, which uses strategy type controls, the weak formulation allows us to consider the game with control against control. We shall prove the existence of game value under natural conditions. Another main feature of the paper is that we allow for non-Markovian structure, and ...

TheMultipleAttribute DecisionMaking (MADM) problem deals with candidate priority alternatives with respect to various attributes. MADM techniques are popularly used in diverse fields such as engineering, economics, management science, transportation planning, etc. Several approaches have been developed for assessing theweights of MADM problems, e.g., the eigenvector method, ELECTRE, TOPSIS, etc...

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...

Kalmar [2, 1928-9] proved that Chess is strictly determined. Von Neumann-Morgenstern [5, 1944] proved the same for any finite two-person zero-sum perfect-information (PI) game. The latter result yields a minimax theorem for (finite) non-zero-sum PI games. Fix a PI, and a player, Ann. Convert this game to a two-person zero-sum game between Ann and the other players (considered as one player), in...

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.

In this paper Boolean games are introduced as a class of two-player zero-sum games along with a number of operations on them. We argue that Boolean games can be interpreted as modelling the information structures of two-person zero-sum games. As such they comprise games of imperfect information. The algebra of Boolean games modulo strategic equivalence is then proven to be isomorphic to the Lin...