Nash Equilibrium Learning In Large Populations With First-Order Payoff Modifications

We establish Nash equilibrium learning in large populations of noncooperative, strategic agents. Our analysis considers the broadest class to date of payoff mechanisms with first-order modifications, capable of modeling bounded rationality and anticipatory effects, averaging, or Pad\'{e} delay approximations. We propose a framework that, for the first time, combines two nonstandard system-theoretic passivity notions. Our results hold for discontinuous best response dynamics alongside continuous learning rules, significantly extending prior work.