Relative Best Response Dynamics in finite and convex Network Games

Conference paper (2019)

Authors

Alain Govaert University Medical Center Groningen, Rijksuniversiteit Groningen
Carlo Cenedese Rijksuniversiteit Groningen
S. Grammatico Team Bart De Schutter - Mechanical, Maritime and Materials Engineering , Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
Ming Cao Rijksuniversiteit Groningen
Research Group
Team Sergio Grammatico (Mechanical, Maritime and Materials Engineering) (TU Delft)
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Published Date

2019

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sergio Grammatico

Abstract

Motivated by theoretical and experimental economics, we propose novel evolutionary dynamics for games on networks, called the h-Relative Best Response (h-RBR) dynamics, that mixes the relative performance considerations of imitation dynamics with the rationality of best responses. Under such a class of dynamics, the players optimize their payoffs over the set of strategies employed by a time-varying subset of their neighbors. As such, the h-RBR dynamics share the defining non-innovative characteristic of imitation based dynamics and can lead to equilibria that differ from classic Nash equilibria. We study the asymptotic behavior of the h-RBR dynamics for both finite and convex games in which the strategy spaces are discrete and compact, respectively, and provide preliminary sufficient conditions for finite-time convergence to a generalized Nash equilibrium.