Robustness of dynamics in games: A contraction mapping decomposition approach

Sina Arefizadeh, Sadegh Arefizadeh, S. Rasoul Etesami, Sadegh Bolouki

Research output: Contribution to journalArticlepeer-review


A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the asymptotic behavior of a given dynamics in a designated game. Although there is a large body of literature on developing convergent dynamics to the Nash equilibrium (NE) of a game, in general, the asymptotic behavior of an underlying dynamics may not be even close to a NE. In this paper, we initiate a new direction toward game dynamics by studying the contraction properties of the map of dynamics in games. To this aim, we first decompose the map of a given dynamics into contractive and non-contractive parts and then explore the asymptotic behavior of those dynamics using the proximity of such decomposition to contraction mappings. In particular, we analyze the non-contractive behavior for better/best response dynamics in discrete-action space sequential/repeated games and show that the non-contractive part of those dynamics is well-behaved in a certain sense. That allows us to estimate the asymptotic behavior of such dynamics using a neighborhood around the fixed point of their contractive part proxy. Finally, we demonstrate the practicality of our framework via an example from the duopoly Cournot games.

Original languageEnglish (US)
Article number111142
StatePublished - Sep 2023
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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