Robustness of dynamics in games: A contraction mapping decomposition approach

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