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.

We propose the sequence form as a new strategic description for an extensive game with perfect recall. It is similar to the normal form but has linear instead of exponential complexity and allows a direct representation and efficient computation of behavior strategies. Pure strategies and their mixed strategy probabilities are replaced by sequences of consecutive choices and their realization p...

We propose the sequence form as a new strategic description for an extensive game with perfect recall. It is similar to the normal form but has linear instead of exponential complexity, and allows a direct representation and eecient computation of behavior strategies. Pure strategies and their mixed strategy probabilities are replaced by sequences of consecutive choices and their realization pr...

Within the framework of stochastic two-person nonzero-sum games, we deal with two commonly used models in engineering and economics-namely, the LQG (Linear-Quadratic-Gaussian) and the duopoly problems. We investigate how variations in information available to either player affect the equilibrium Nash strategies for these two models, whose existence and uniqueness have been proven in the paper. ...

In a repeated zero-sum two-person game with incomplete information on both sides, the asymptotic value is defined as v = lim_oo v", where vn is the value of the game with n repetitions. It is shown here that v may be a transcendental number even for games in which all parameters defining the game are rational. This is in contrast to the situation in stochastic games where by the result of Bewle...

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). While not every two-person zero-sum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the...

This study proposes a novel way to deal with uncertainty in two-person zero-sum matrix game payoffs expressed as fuzzy rough numbers. Complete and reasonable solutions these types of games are obtained. In this research we develop two linear programming models upper lower approximation intervals numbers handle multi-objective crisp by incorporating trapezoidal payoffs. To provide each opponent ...