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Identifying level-k reasoning in repeated games: Strategies, beliefs, and cognitive ability

Author

Listed:
  • Gill, David

    (Purdue University)

  • Rosokha, Yaroslav

    (Purdue University)

Abstract

In this paper, we identify level-k reasoning in repeated games that operates at the level of a supergame strategy, rather than at the level of individual rounds. First, we develop a model of level-k reasoning that incorporates choices over strategies as well as beliefs about strategies chosen by others. Then, using data from the Indefinitely Repeated Prisoner's Dilemma that includes elicited strategies and beliefs about strategies, we classify a substantial fraction of subjects as level-1 or level-2. Moreover, we show that when level-k reasoning operates at the level of a strategy, cognitive ability and experience both predict higher level reasoning.

Suggested Citation

  • Gill, David & Rosokha, Yaroslav, 2026. "Identifying level-k reasoning in repeated games: Strategies, beliefs, and cognitive ability," CAGE Online Working Paper Series 788, Competitive Advantage in the Global Economy (CAGE).
    • Handle: RePEc:cge:wacage:788
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/cage/manage/publications/wp788.2026.pdf
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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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