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Smooth solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...

Smooth Solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be...

Solidarity and cooperative bargaining solutions

Naoki Yoshihara (2006)

Banach Center Publications

In this paper, we consider production economies with possibly unequal production skills and with the possibility of technological innovations, in which resource allocations are determined via bargaining among individuals. We define the Nash (resp. the Kalai-Smorodinsky) bargaining solution as the (bargaining) allocation rule whose utility outcomes just result in the Nash (resp. the Kalai-Smorodinsky) bargaining outcomes. Two new axioms regarding compensation for low skill agents are introduced as...

Solution set in a special case of generalized Nash equilibrium games

Josef Cach (2001)

Kybernetika

A special class of generalized Nash equilibrium problems is studied. Both variational and quasi-variational inequalities are used to derive some results concerning the structure of the sets of equilibria. These results are applied to the Cournot oligopoly problem.

Solving multi-objective fuzzy matrix games via multi-objective linear programming approach

Abha Aggarwal, Imran Khan (2016)

Kybernetika

A class of multi-objective fuzzy matrix games is studied and it is shown that solving such a game is equivalent to solving a pair of multi-objective linear programming problems. This work generalizes an earlier study of Fernandez et al. [7] from crisp scenario to fuzzy scenario on the lines of Bector et al. [4]. Further certain difficulties with similar studies reported in the literature are also discussed.

Some applications of the point-open subbase game

D. Guerrero Sánchez, Vladimir Vladimirovich Tkachuk (2017)

Commentationes Mathematicae Universitatis Carolinae

Given a subbase 𝒮 of a space X , the game P O ( 𝒮 , X ) is defined for two players P and O who respectively pick, at the n -th move, a point x n X and a set U n 𝒮 such that x n U n . The game stops after the moves { x n , U n : n ø } have been made and the player P wins if n ø U n = X ; otherwise O is the winner. Since P O ( 𝒮 , X ) is an evident modification of the well-known point-open game P O ( X ) , the primary line of research is to describe the relationship between P O ( X ) and P O ( 𝒮 , X ) for a given subbase 𝒮 . It turns out that, for any subbase 𝒮 , the player P has a winning strategy...

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