2017/07/19 by Brian Swenson, Swenson, Brian, Ryan Murray +3
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #37B25 #91A06 #91A26 #93A14 #93A15 #Economic theories and models #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Multiagent Systems (cs.MA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1707.06465
openalex publication_date 2017/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper studies the convergence properties of (continuous) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understood in many games of interest due to the discontinuous, set-valued nature of the best-response map. The paper focuses on elucidating several important properties of best-response dynamics in the class of multi-agent games known as potential games---a class of games with fundamental importance in multi-agent systems and distributed control. It is shown that in almost every potential game and for almost every initial condition, the best-response dynamics (i) have a unique solution, (ii) converge to pure-strategy Nash equilibria, and (iii) converge at an exponential rate.