We consider linear generalized Nash games and introduce the socalled cone condition which characterizes the smoothness of the Nikaido-Isoda function under weak assumptions. The latter mapping arises from a reformulation of the generalized Nash equilibrium problem as a possibly nonsmooth optimization problem. Other regularity conditions like LICQ or SMFC(Q) are only sufficient for smoothness, bu...

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...

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadra...

The Gale–Nikaido–Debreu lemma plays an important role in establishing the existence of competitive equilibrium. In this paper, we use Sperner’s and basic elements topology to prove lemma.

We establish common fixed point theorems related with families of selfmappings on metric spaces. Our results extend, improve, and unify the results due to Fisher (1977, 1978, 1979, 1981, 1984), Jungck (1988), and Ohta and Nikaido (1994). 2000 Mathematics Subject Classification. 47H10, 54H25.

Dzwokai Wla,̂ '̂ David N. Cook,^ Wlarie Albert!,^ NingG. Pon,^ Hiroshi Nikaido'̂ '* and John E. 'Department of Chemistry, University of Gatlfornia, Berkeley, California 94720. USA. ^Division of Structural Biology. Lawrence Berkeley Laboratory, Berkeley. California 94720. USA. '^Sferitech inc., 2525 Stanwell Drive, Suite 300, Concord, California 94520, USA. '^Department of Molecular and Cell Biolog...

Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta and Nikaido in 1994.