IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v143y2008i1p216-250.html
   My bibliography  Save this article

Trees and extensive forms

Author

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

Abstract

This paper addresses the question of what it takes to obtain a well-defined extensive form game. Without relying on simplifying finiteness or discreteness assumptions, we characterize the class of game trees for which all pure strategy combinations induce unique outcomes. The generality of the set-up covers "exotic" cases, like stochastic games or decision problems in continuous time (differential games). We find that the latter class, though a well-defined problem, fails this test.

Suggested Citation

  • Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    • Handle: RePEc:eee:jetheo:v:143:y:2008:i:1:p:216-250
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(08)00028-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    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. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    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. Simon, Leo K. & Stinchcombe, Maxwell B., 1987. "Extensive From Games in Continuous Time: Pure Strategies," Department of Economics, Working Paper Series qt03x115sh, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    5. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    6. Stinchcombe, Maxwell B., 1992. "Maximal strategy sets for continuous-time game theory," Journal of Economic Theory, Elsevier, vol. 56(2), pages 235-265, April.
    7. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    8. Friedman, Avner, 1994. "Differential games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 22, pages 781-799, Elsevier.
    9. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
      • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
    10. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
    11. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    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. Jan-Henrik Steg, 2018. "On Preemption in Discrete and Continuous Time," Dynamic Games and Applications, Springer, vol. 8(4), pages 918-938, December.
    2. Niko Jaakkola & Florian Wagener, 2020. "All symmetric equilibria in differential games with public goods," Tinbergen Institute Discussion Papers 20-020/II, Tinbergen Institute.
    3. Staudigl, Mathias & Steg, Jan-Henrik, 2014. "On Repeated Games with Imperfect Public Monitoring: From Discrete to Continuous Time," Center for Mathematical Economics Working Papers 525, Center for Mathematical Economics, Bielefeld University.
    4. 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.
    5. Alós-Ferrer, Carlos & Prat, Julien, 2012. "Job market signaling and employer learning," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1787-1817.
    6. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    7. 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.
    8. Attila Ambrus & Shih En Lu, 2015. "A Continuous-Time Model of Multilateral Bargaining," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 208-249, February.
    9. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    10. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    11. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    12. Santiago R. Balseiro & Omar Besbes & Gabriel Y. Weintraub, 2019. "Dynamic Mechanism Design with Budget-Constrained Buyers Under Limited Commitment," Operations Research, INFORMS, vol. 67(3), pages 711-730, May.
    13. 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.
    14. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    15. 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.
    16. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizations of perfect recall," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 311-326, May.
    17. Alós-Ferrer, Carlos & Kern, Johannes, 2015. "Repeated games in continuous time as extensive form games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 34-57.
    18. 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.
    19. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.

    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. E. Emanuel Rapsch, 2024. "Decision making in stochastic extensive form II: Stochastic extensive forms and games," Papers 2411.17587, arXiv.org.
    2. 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.
    3. Alós-Ferrer, Carlos & Kern, Johannes, 2015. "Repeated games in continuous time as extensive form games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 34-57.
    4. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.
    5. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    6. Anbarci, Nejat & Feltovich, Nick, 2018. "How fully do people exploit their bargaining position? The effects of bargaining institution and the 50–50 norm," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 320-334.
    7. Nobuo Koida, 2018. "Anticipated stochastic choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 545-574, May.
    8. Lambert, Eve-Angéline & Peterle, Emmanuel & Tisserand, Jean-Christian, 2019. "Pretrial settlement and coercion: An experiment," International Review of Law and Economics, Elsevier, vol. 60(C).
    9. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
    10. Ortner, Juan, 2019. "A continuous-time model of bilateral bargaining," Games and Economic Behavior, Elsevier, vol. 113(C), pages 720-733.
    11. Faruk Gul & Wolfgang Pesendorfer, 2004. "Self Control, Revealed Preferences and Consumption Choice," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(2), pages 243-264, April.
    12. Mitri Kitti, 2014. "Equilibrium Payoffs for Pure Strategies in Repeated Games," Discussion Papers 98, Aboa Centre for Economics.
    13. Radner, Roy, 2003. "Viscous demand," Journal of Economic Theory, Elsevier, vol. 112(2), pages 189-231, October.
      • Roy Radner, 1999. "Viscous Demand," Working Papers 99-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    14. E. Emanuel Rapsch, 2024. "Decision making in stochastic extensive form I: Stochastic decision forests," Papers 2404.12332, arXiv.org, revised Nov 2024.
    15. Xue, Lian & Sitzia, Stefania & Turocy, Theodore L., 2023. "Concord and contention in a dynamic unstructured bargaining experiment with costly conflict," Journal of Economic Psychology, Elsevier, vol. 97(C).
    16. Urmee Khan & Maxwell B. Stinchcombe, 2015. "The Virtues of Hesitation: Optimal Timing in a Non-stationary World," American Economic Review, American Economic Association, vol. 105(3), pages 1147-1176, March.
    17. Nejat Anbarci & Nick Feltovich, 2013. "How sensitive are bargaining outcomes to changes in disagreement payoffs?," Experimental Economics, Springer;Economic Science Association, vol. 16(4), pages 560-596, December.
    18. Lones Smith & Ennio Stacchetti, 2002. "Aspirational Bargaining," Game Theory and Information 0201003, University Library of Munich, Germany.
    19. Z. Eddie Ning, 2021. "List Price and Discount in a Stochastic Selling Process," Marketing Science, INFORMS, vol. 40(2), pages 366-387, March.
    20. Mitri Kitti, 2018. "Subgame Perfect Equilibria in Continuous-Time Repeated Games," Discussion Papers 120, Aboa Centre for Economics.

    More about this item

    Keywords

    Extensive forms Trees Sequential decision theory Differential games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    Statistics

    Access and download statistics

    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:jetheo:v:143:y:2008:i:1:p:216-250. 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/inca/622869 .

    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.