IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v62y2016icp5-18.html
   My bibliography  Save this article

Equilibrium existence for large perfect information games

Author

Listed:
  • Alós-Ferrer, Carlos
  • Ritzberger, Klaus

Abstract

This paper provides a novel existence theorem for subgame perfect equilibria of potentially large extensive form games with perfect information and continuous preferences, allowing for infinite horizon and infinite action spaces. The approach is based on the properties of the topology on the space of outcomes and differs from all previous approaches in the literature. Furthermore, the existence proof relies on a new algorithm that is independent of the horizon, hence can also be applied to infinite-horizon games.

Suggested Citation

  • Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
  • Handle: RePEc:eee:mateco:v:62:y:2016:i:c:p:5-18
    DOI: 10.1016/j.jmateco.2015.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406815001238
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmateco.2015.10.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    3. David K. Levine & Drew Fudenberg, 2006. "A Dual-Self Model of Impulse Control," American Economic Review, American Economic Association, vol. 96(5), pages 1449-1476, December.
    4. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 75-102, January.
    5. Drew Fudenberg & David K. Levine, 2012. "Timing and Self‐Control," Econometrica, Econometric Society, vol. 80(1), pages 1-42, January.
    6. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eilon Solan & Koos Vrieze, 2010. "Perfect-Information Games with Lower-Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 742-755, November.
    7. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    8. J. Flesch & J. Kuipers & G. Schoenmakers & K. Vrieze, 2010. "Subgame Perfection in Positive Recursive Games with Perfect Information," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 193-207, February.
    9. Faruk Gul & Wolfgang Pesendorfer, 2004. "Self-Control and the Theory of Consumption," Econometrica, Econometric Society, vol. 72(1), pages 119-158, January.
    10. 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.
    11. 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.
    12. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Comment," Econometrica, Econometric Society, vol. 71(6), pages 1909-1911, November.
    13. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    14. Roger A. Purves & William D. Sudderth, 2011. "Perfect Information Games with Upper Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 468-473, August.
    15. Hellwig, Martin & Leininger, Wolfgang, 1987. "On the existence of subgame-perfect equilibrium in infinite-action games of perfect information," Journal of Economic Theory, Elsevier, vol. 43(1), pages 55-75, October.
    16. Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
    17. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-544, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aviad Heifetz & Enrico Minelli & Herakles Polemarchakis, 2021. "Liberal parentalism," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(6), pages 1107-1129, December.
    2. 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.
    3. János Flesch & Arkadi Predtetchinski, 2017. "A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1162-1179, November.
    4. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    5. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
    6. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    7. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    8. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    9. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
    2. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    3. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    4. Wei He & Yeneng Sun, 2015. "Dynamic Games with Almost Perfect Information," Papers 1503.08900, arXiv.org.
    5. Duggan, John, 2017. "Existence of stationary bargaining equilibria," Games and Economic Behavior, Elsevier, vol. 102(C), pages 111-126.
    6. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    7. He, Wei & Sun, Yeneng, 2015. "Dynamic Games with Almost Perfect Information," MPRA Paper 63345, University Library of Munich, Germany.
    8. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    9. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    10. Flesch, Janos & Herings, P. Jean-Jacques & Maes, Jasmine & Predtetchinski, Arkadi, 2019. "Individual upper semicontinuity and subgame perfect ϵ-equilibria in games with almost perfect information," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Julio González-Díaz & Miguel Meléndez-Jiménez, 2014. "On the notion of perfect Bayesian equilibrium," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 128-143, April.
    12. Mariotti, Thomas, 2000. "Subgame-perfect equilibrium outcomes in continuous games of almost perfect information1," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 99-128, August.
    13. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    14. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2022. "Individual upper semicontinuity and subgame perfect $$\epsilon $$ ϵ -equilibria in games with almost perfect information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 695-719, April.
    15. János Flesch & Arkadi Predtetchinski, 2017. "A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1162-1179, November.
    16. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-perfect $$\epsilon $$ ϵ -equilibria in perfect information games with sigma-discrete discontinuities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 479-495, March.
    17. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eran Shmaya & Eilon Solan & Koos Vrieze, 2014. "Non-existence of subgame-perfect $$\varepsilon $$ ε -equilibrium in perfect information games with infinite horizon," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 945-951, November.
    18. Jeroen Kuipers & János Flesch & Gijs Schoenmakers & Koos Vrieze, 2021. "Subgame perfection in recursive perfect information games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 603-662, March.
    19. Peysakhovich, Alexander, 2014. "How to commit (if you must): Commitment contracts and the dual-self model," Journal of Economic Behavior & Organization, Elsevier, vol. 101(C), pages 100-112.
    20. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:62:y:2016:i:c:p:5-18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.