The generalized Nash equilibrium problem is a Nash game which, in contrast to the standard Nash equilibrium problem, allows the strategy sets of each player to depend on the decision variables of all other players. It was recently shown by the authors that this generalized Nash equilibrium problem can be reformulated as both an unconstrained and a constrained optimization problem with continuou...

With the overexploitation of many conventional fish stocks, and growing interest in harvesting new kinds of food from the sea, there is an increasing need for managers of fisheries to take account of interactions among species. In this work we define a bioeconomic equilibrium model for ’n’ fishermen who catch three species; these species compete with each other for space or food. The natural gr...

We revisit the problem of real-time pricing for load frequency balancing introduced in [3]. Taking inspiration from the Vickrey-Clarke-Groves (VCG) mechanism, we derive incremental price functions that implement the optimal solution in Nash equilibrium. We then compare this pricing scheme with some recent dynamic mechanisms.

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of so...

This paper addresses the similarity assessment and the retrieval problems in Case-Based Reasoning for case bases consisting of traditional and generalized cases. Previous work focussed on similarity assessment for generalized cases with continuous domains. The similarity assessment problem was formulated as Nonlinear Programm (NLP), which is well known in mathematical optimization. In several r...

We define the logit dynamic for games with continuous strategy spaces and establish its fundamental properties , i.e. the existence, uniqueness and continuity of solutions. We apply the dynamic to the analysis of the Burdett and Judd (1983) model of price dispersion. Our objective is to assess the stability of the logit equilibrium corresponding to the unique Nash equilibrium of this model. Alt...

In this paper, we introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions, some strong convergence theorems are established. The results obtained in this paper are new, and a few examples illustrat...

This paper examines leader-follower games where a leader must purchase an essential input from a price-setting supplier in order to take an action. We show that equilibrium outcomes when the followers perfectly observe the leaders’actions cannot be approximated by mixed equilibrium outcomes of the game where followers imperfectly observe the leaders’actions, i.e. they are not accessible. Access...

The purpose of this paper is to introduce and investigate a more generalized hybrid shrinking projection algorithm for finding a common solution for a system of generalized mixed equilibrium problems. A accelerated strong convergence theorem of common solutions is established in the framework of a non-uniformly convex Banach space. These new results improve and extend the previously known ones ...