Contributed Session Wed.1.MA 043

Wednesday, 10:30 - 12:00 h, Room: MA 043

Cluster 8: Game theory [...]

Variational inequalities in games


Chair: Vikas Kumar Jain



Wednesday, 10:30 - 10:55 h, Room: MA 043, Talk 1

Evgeniy Golshtein
Many-person games with convex structure


The set of Nash equilibrium points of a non-cooperative
many-person game coincides with the solution set of a
variational inequality associated with this game. The
game is said to have a convex structure if the above
mentioned variational inequality is defined by a monotone
mapping. The convex-structure games can be solved by
efficient numerical methods. The paper presents a
sufficient condition to guarantee a game to have a
convex structure. For finite games in mixed strategies,
the author gives an equivalent form of this condition
in terms of the tables defining the game. Moreover, for
the class of finite games, it is demonstrated that the
proposed condition is not only sufficient but also
necessary for the convex-structure games.



Wednesday, 11:00 - 11:25 h, Room: MA 043, Talk 2

Vikas Kumar Jain
Constrained vector-valued dynamic game and symmetric duality for multiobjective variational problems


A certain constrained vector-valued dynamic game is formulated and shown to be equivalent to a pair of multiobjective symmetric dual variational problems which have more general formulations than those studied earlier. A number of duality theorems, are established under suitable generalized convexity assumptions on the functionals. This constrained vector-valued dynamic game is also regarded as equivalent to a pair of symmetric multiobjective dual variational problems with natural boundary conditions rather than fixed end points. Finally, it is also indicated that our results can be considered as dynamic generalization of those already studied in the literature.


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