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Equivalence between graph-based and sequence-based extensive form games

Author

Listed:
  • J. Jude Kline

    (University of Queensland)

  • Shravan Luckraz

    (University of Nottingham)

Abstract

This note establishes an equivalence between the graph-based definition of an infinite extensive form game [following Kuhn (Contributions to the theory of games II, Princeton: Princeton University Press, pp 193–216, 1953)] and the sequence-based definition by Osborne and Rubinstein (A course in game theory, Cambridge: MIT Press, 1994).

Suggested Citation

  • J. Jude Kline & Shravan Luckraz, 2016. "Equivalence between graph-based and sequence-based extensive form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 85-94, April.
    • Handle: RePEc:spr:etbull:v:4:y:2016:i:1:d:10.1007_s40505-016-0094-z
    DOI: 10.1007/s40505-016-0094-z
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    References listed on IDEAS

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    1. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
    2. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    3. Carlos Alós-Ferrer & Klaus Ritzberger, 2005. "Trees and decisions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 763-798, June.
    4. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    5. Mamoru Kaneko & J. Kline, 2013. "Partial memories, inductively derived views, and their interactions with behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 27-59, May.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    7. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
    8. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
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    Citations

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    Cited by:

    1. Subir K. Chakrabarti & Iryna Topolyan, 2016. "An extensive form-based proof of the existence of sequential equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 355-365, October.
    2. Shravan Luckraz, 2019. "A Survey on the Relationship Between the Game of Cops and Robbers and Other Game Representations," Dynamic Games and Applications, Springer, vol. 9(2), pages 506-520, June.
    3. Peter A. Streufert, 2018. "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms," University of Western Ontario, Departmental Research Report Series 20186, University of Western Ontario, Department of Economics.
    4. Peter A. Streufert, 2020. "The Category of Node-and-Choice Extensive-Form Games," Papers 2004.11196, arXiv.org, revised Jul 2020.
    5. Peter A. Streufert, 2019. "Equivalences among five game specifications, including a new specification whose nodes are sets of past choices," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 1-32, March.
    6. Shravan Luckraz & Bruno Antonio Pansera, 2022. "A Note on the Concept of Time in Extensive Games," Mathematics, MDPI, vol. 10(8), pages 1-4, April.

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    More about this item

    Keywords

    Extensive form games; Equivalence theorems; Graph theory;
    All these keywords.

    JEL classification:

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

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