Open AccessThe replicator dynamics of generalized Nash games
Author(s) -
Jason Lequyer,
Monica–Gabriela Cojocaru
Publication year - 2021
Publication title -
mathematics in applied sciences and engineering
Language(s) - English
Resource type - Journals
ISSN - 2563-1926
DOI - 10.5206/mase/11137
Subject(s) - replicator equation , nash equilibrium , mathematical economics , evolutionary dynamics , evolutionarily stable strategy , evolutionary game theory , selection (genetic algorithm) , computer science , best response , game theory , natural selection , mathematics , mathematical optimization , artificial intelligence , sociology , population , demography
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.