Taming selten's horse with impulse response☆

• 成果类型: Article
• 署名作者: Neugebauer, Tibor; Sadrieh, Abdolkarim; Selten, Reinhard
• 署名单位: University of Luxembourg; Otto von Guericke University; University of Bonn
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2024.11.014
• 发表日期: 2025
• 页码: 71-92
• 关键词: Trembling-hand Perfect Equilibrium; Game of Selten's Horse; Learning Direction Theory; Impulse Response Dynamics; quantal response; Reinforcement Learning; Level-k

摘要

The paper experimentally examines the predictive power of the trembling-hand perfect equilibrium concept in the three-player Game of Selten's Horse. At first sight, our data show little support of the trembling-hand perfect equilibrium and rather favor the imperfect equilibrium. We introduce deterministic impulse response trajectories that converge on the trembling-hand perfect equilibrium. The impulse response trajectories are remarkably close - closer than the trajectories from a reinforcement learning model - to the observed dynamics of the game in the short run (50 periods). The quantal response approach also converges on the trembling-hand perfect equilibrium as the error rates decline, suggesting that the trembling-hand perfect equilibrium may be reached in the long run. In the long run (up to 250 periods), however, behavior seems to settle at a non-equilibrium distribution of strategies that rather supports efficient outcomes, instead of converging to the trembling-hand perfect equilibrium.