Best-response dynamics, playing sequences, and convergence to equilibrium in random games

Arbeitspapier

We show that the playing sequence-the order in which players update their actions-is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random n-player m-action games under three distinct playing sequences: clockwork sequences (players take turns according to a fixed cyclic order), random sequences, and simultaneous updating by all players. We analytically characterize the convergence properties of the clockwork sequence best-response dynamic. Our key asymptotic result is that this dynamic almost never converges to a pure Nash equilibrium when n and m are large. By contrast, the random sequence best- response dynamic converges almost always to a pure Nash equilibrium when one exists and n and m are large. The clockwork best-response dynamic deserves particular attention: we show through simulation that, compared to random or simultaneous updating, its convergence properties are closest to those exhibited by three popular learning rules that have been calibrated to human game-playing in experiments (reinforcement learning, fictitious play, and replicator dynamics).

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: LEM Working Paper Series ; No. 2021/02

Classification and Topics

• Classification: Wirtschaft ; Existence and Stability Conditions of Equilibrium ; Noncooperative Games ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
• Subject: Best-response dynamics ; equilibrium convergence ; random games ; learning models in games

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Heinrich, Torsten ; Jang, Yoojin ; Mungo, Luca ; Pangallo, Marco ; Scott, Alex ; Tarbush, Bassel ; Wiese, Samuel
• Event: Veröffentlichung
• (who): Scuola Superiore Sant'Anna, Laboratory of Economics and Management (LEM)
• (where): Pisa
• (when): 2021

Further information

• Handle: http://hdl.handle.net/10419/243498
• Last update: 10.03.2025, 11:44 AM CET