Taming selten's horse with impulse response

Tibor Neugebauer, Abdolkarim Sadrieh and Reinhard Selten

Games and Economic Behavior, 2025, vol. 150, issue C, 71-92

Abstract: 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.

Keywords: Trembling-hand Perfect Equilibrium; Game of Selten's Horse; Learning Direction Theory; Impulse Response Dynamics; Quantal Response; Reinforcement Learning; Level-k (search for similar items in EconPapers)
JEL-codes: C90 D53 D92 G02 G11 G12 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:150:y:2025:i:c:p:71-92

DOI: 10.1016/j.geb.2024.11.014

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