Memoryless Algorithmic Collusion: Sure to Fail, Slow to Fall

Zhang Xu and Wei Zhao

Papers from arXiv.org

Abstract: This paper shows that, in a class of Bertrand-style competition games, memoryless Q-learning algorithms should adapt to Nash Equilibrium given sufficient explorations in the long-run. This is also verified through accelerating simulations, while the convergence time grows super-exponentially for high discount factors. The resilience of collusive outcomes in the short-run is due to exploration of unprofitable actions, making the system resemble random walk. A structural model is proposed to estimate the convergence time, which not only explains the role of discount factor, but also unveils the non-monotonic relation in learning rate, which is overlooked in the literature.

Date: 2024-09, Revised 2026-08
New Economics Papers: this item is included in nep-ain, nep-com, nep-des, nep-gth and nep-mic
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