We consider the generalized Nash equilibrium problem which, in contrast to the standard Nash equilibrium problem, allows joint constraints of all players involved in the game. Using a regularized Nikaido-Isoda-function, we then present three optimization problems related to the generalized Nash equilibrium problem. The first optimization problem is a complete reformulation of the generalized Na...

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a so...

We generalize the P, P0, R0 properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of generalized nonlinear complementarity problem (GNCP). We prove that if a continuous function has the order P0 and R0 properties then all the associated GNCPs have solutions.

Nash’s theorem guarantees the presence of mixed nash equilibrium in every finite game. We are concerned here with the problem of finding such an equilibrium efficiently. In other words, does there exist an algorithm to find the mixed nash equilibrium in polynomial time? The answer to this question is not known but it is known finding mixed Nash equilibrium is PPAD complete, which implies some s...

In this paper, we introduce a new iterative sequence which is constructed by using the hybrid projection method for solving the common solution for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain the conditions, the common solution for the families of quasi -φasymptotically nonexpansive and uniformly Lipschitz con...