Generalized Nash games and quasi-variational inequalities

1991 ◽  
Vol 54 (1) ◽  
pp. 81-94 ◽  
Author(s):  
Patrick T. Harker
Keyword(s):  
Variational Inequalities ◽  
Nash Games ◽  
Generalized Nash Games

On generalized Nash games and variational inequalities

2007 ◽  
Vol 35 (2) ◽  
pp. 159-164 ◽  
Author(s):  
Francisco Facchinei ◽  
Andreas Fischer ◽  
Veronica Piccialli
Keyword(s):  
Variational Inequalities ◽  
Nash Games ◽  
Generalized Nash Games

scholarly journals On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 266 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Nash Games ◽  
New Class ◽  
Set Valued Mappings ◽  
Differential Variational Inequalities ◽  
Theoretical Developments

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

A Note on Generalized Nash Games Played on Networks

2021 ◽  
pp. 365-380
Author(s):  
Mauro Passacantando ◽  
Fabio Raciti
Keyword(s):  
Nash Games ◽  
Generalized Nash Games

scholarly journals The replicator dynamics of generalized Nash games

2021 ◽  
pp. 1-15
Author(s):  
Jason Lequyer ◽  
Monica-Gabriela Cojocaru
Keyword(s):  
Replicator Dynamics ◽  
Evolutionary Games ◽  
Replicator Equation ◽  
Nash Games ◽  
Phenotypic Changes ◽  
Generalized Nash Games ◽  
The Past ◽  
Interacting Populations ◽  
Common Framework ◽  
The Relationship

Generalized Nash Games are a powerful modelling tool, first introduced in the 1950's. They have seen some important developments in the past two decades. Separately, Evolutionary Games were introduced in the 1960's and seek to describe how natural selection can drive phenotypic changes in interacting populations. In this paper, we show how the dynamics of these two independently formulated models can be linked under a common framework and how this framework can be used to expand Evolutionary Games. At the center of this unified model is the Replicator Equation and the relationship we establish between it and the lesser known Projected Dynamical System.

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