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Behavioral Equivalence of Extensive Game Structures

Author

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  • Pierpaolo Battigalli
  • Paolo Leonetti
  • Fabio Maccheroni

Abstract

Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced strategies to induced terminal paths. We show that this is the case if and only if one can be transformed into the other through a composition of two elementary transformations, commonly known as “Interchanging of Simultaneous Moves†and “Coalescing Moves/Sequential Agent Splitting.â€

Suggested Citation

  • Pierpaolo Battigalli & Paolo Leonetti & Fabio Maccheroni, 2019. "Behavioral Equivalence of Extensive Game Structures," Working Papers 655, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:652
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    2. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    3. Lin, Po-Hsuan & Palfrey, Thomas R., 2024. "Cognitive hierarchies for games in extensive form," Journal of Economic Theory, Elsevier, vol. 220(C).
    4. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
    5. Ritzberger, Klaus & Weibull, Jörgen W. & Wikman, Peter, 2025. "Solid outcomes in finite games," Journal of Economic Theory, Elsevier, vol. 224(C).
    6. Carlos Alós-Ferrer & Klaus Ritzberger, 2020. "Reduced normal forms are not extensive forms," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 281-288, October.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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