IDEAS home Printed from https://ideas.repec.org/p/mib/wpaper/289.html
   My bibliography  Save this paper

Limited backward induction: foresight and behavior in sequential games

Author

Listed:
  • Marco Mantovani

Abstract

The paper tests experimentally for limited foresight in sequential games. We develop a general out-of-equilibrium framework of strategic thinking based on limited foresight. It assumes the players take decisions focusing on close-by nodes, following backward induction – what we call limited backward induction (LBI). The main prediction of the model is tested in the context of a modified Game of 21. In line with the theoretical hypotheses, our results show most players think strategically only on close-by nodes without reasoning backwards from the end of the game. A small fraction of subjects play close to equilibrium, while few others try to exploit the limited foresight of their opponent. The results provide strong support for LBI, and cannot be accounted for using the most popular models of strategic thinking, let alone equilibrium analysis.

Suggested Citation

  • Marco Mantovani, 2015. "Limited backward induction: foresight and behavior in sequential games," Working Papers 289, University of Milano-Bicocca, Department of Economics, revised Jan 2015.
    • Handle: RePEc:mib:wpaper:289
    as

    Download full text from publisher

    File URL: http://repec.dems.unimib.it/repec/pdf/mibwpaper289.pdf
    File Function: First version, 2015
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Binmore, Ken & McCarthy, John & Ponti, Giovanni & Samuelson, Larry & Shaked, Avner, 2002. "A Backward Induction Experiment," Journal of Economic Theory, Elsevier, vol. 104(1), pages 48-88, May.
    2. Thomas Dohmen & Armin Falk & David Huffman & Uwe Sunde & Jürgen Schupp & Gert G. Wagner, 2011. "Individual Risk Attitudes: Measurement, Determinants, And Behavioral Consequences," Journal of the European Economic Association, European Economic Association, vol. 9(3), pages 522-550, June.
    3. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    4. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
    5. Larbi Alaoui & Antonio Penta, 2016. "Endogenous Depth of Reasoning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1297-1333.
    6. Theodoros M. Diasakos, 2008. "Complexity and Bounded Rationality in Individual Decision Problems," Carlo Alberto Notebooks 90, Collegio Carlo Alberto.
    7. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    8. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May.
    9. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    10. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    11. Ciril Bosch-Rosa & Thomas Meissner & Antoni Bosch-Domènech, 2018. "Cognitive bubbles," Experimental Economics, Springer;Economic Science Association, vol. 21(1), pages 132-153, March.
    12. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 132-143, August.
    13. Mengel, Friederike, 2014. "Learning by (limited) forward looking players," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 59-77.
    14. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    15. Bonanno, Giacomo, 2001. "Branching Time, Perfect Information Games, and Backward Induction," Games and Economic Behavior, Elsevier, vol. 36(1), pages 57-73, July.
    16. Teck-Hua Ho & Xuanming Su, 2013. "A Dynamic Level-k Model in Sequential Games," Management Science, INFORMS, vol. 59(2), pages 452-469, March.
    17. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
    18. Paolo Crosetto & Marco Mantovani, 2012. "Availability of Information and Representation Effects in the Centipede Game," Jena Economics Research Papers 2012-051, Friedrich-Schiller-University Jena.
    19. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    20. Cooper, David J. & Van Huyck, John B., 2003. "Evidence on the equivalence of the strategic and extensive form representation of games," Journal of Economic Theory, Elsevier, vol. 110(2), pages 290-308, June.
    21. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    22. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
    23. Theodoros M. Diasakos, 2008. "Complexity and Bounded Rationality in Individual Decision Problems," Carlo Alberto Notebooks 90, Collegio Carlo Alberto.
    24. Steven D. Levitt & John A. List & Sally E. Sadoff, 2011. "Checkmate: Exploring Backward Induction among Chess Players," American Economic Review, American Economic Association, vol. 101(2), pages 975-990, April.
    25. Gneezy, Uri & Rustichini, Aldo & Vostroknutov, Alexander, 2010. "Experience and insight in the Race game," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 144-155, August.
    26. Marcus Dittrich & Kristina Leipold, 2014. "Gender Differences in Strategic Reasoning," CESifo Working Paper Series 4763, CESifo.
    27. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    28. Johnson, Eric J. & Camerer, Colin & Sen, Sankar & Rymon, Talia, 2002. "Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, Elsevier, vol. 104(1), pages 16-47, May.
    29. Shaun Hargreaves Heap & David Rojo Arjona & Robert Sugden, 2014. "How Portable Is Level‐0 Behavior? A Test of Level‐k Theory in Games With Non‐Neutral Frames," Econometrica, Econometric Society, vol. 82(3), pages 1133-1151, May.
    30. Kawagoe, Toshiji & Takizawa, Hirokazu, 2012. "Level-k analysis of experimental centipede games," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 548-566.
    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. Dufwenberg, Martin & Van Essen, Matt, 2018. "King of the Hill: Giving backward induction its best shot," Games and Economic Behavior, Elsevier, vol. 112(C), pages 125-138.
    2. Kirchsteiger, Georg & Mantovani, Marco & Mauleon, Ana & Vannetelbosch, Vincent, 2016. "Limited farsightedness in network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 97-120.
    3. Buser, Thomas & van den Assem, Martijn J. & van Dolder, Dennie, 2023. "Gender and willingness to compete for high stakes," Journal of Economic Behavior & Organization, Elsevier, vol. 206(C), pages 350-370.
    4. Matthew Embrey & Guillaume R Fréchette & Sevgi Yuksel, 2018. "Cooperation in the Finitely Repeated Prisoner’s Dilemma," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 509-551.
    5. Ulrich Bergmann & Arkady Konovalov, 2024. "Auction design and order of sale with budget-constrained bidders," Experimental Economics, Springer;Economic Science Association, vol. 27(1), pages 36-57, March.
    6. Ke, Shaowei, 2019. "Boundedly rational backward induction," Theoretical Economics, Econometric Society, vol. 14(1), January.

    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. Rampal, Jeevant, 2022. "Limited Foresight Equilibrium," Games and Economic Behavior, Elsevier, vol. 132(C), pages 166-188.
    2. García-Pola, Bernardo & Iriberri, Nagore & Kovářík, Jaromír, 2020. "Non-equilibrium play in centipede games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 391-433.
    3. Yun Wang, 2015. "Belief and Higher-Order Belief in the Centipede Games: Theory and Experiment," Working Papers 2015-03-24, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Dan Levin & Luyao Zhang, 2022. "Bridging Level-K to Nash Equilibrium," Papers 2202.12292, arXiv.org, revised Feb 2022.
    5. Dufwenberg, Martin & Van Essen, Matt, 2018. "King of the Hill: Giving backward induction its best shot," Games and Economic Behavior, Elsevier, vol. 112(C), pages 125-138.
    6. Oren Bar-Gill & Christoph Engel, 2020. "Property is Dummy Proof: An Experiment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2020_02, Max Planck Institute for Research on Collective Goods.
    7. Spenkuch, Jörg, 2014. "Backward Induction in the Wild: Evidence from the U.S. Senate," MPRA Paper 58766, University Library of Munich, Germany.
    8. Steven D. Levitt & John A. List & Sally E. Sadoff, 2011. "Checkmate: Exploring Backward Induction among Chess Players," American Economic Review, American Economic Association, vol. 101(2), pages 975-990, April.
    9. Brosig-Koch, Jeannette & Heinrich, Timo & Helbach, Christoph, 2015. "Exploring the capability to reason backwards: An experimental study with children, adolescents, and young adults," European Economic Review, Elsevier, vol. 74(C), pages 286-302.
    10. Sheen S. Levine & Mark Bernard & Rosemarie Nagel, 2018. "Strategic intelligence: The cognitive capability to anticipate competitor behaviour," Strategic Management Journal, Wiley Blackwell, vol. 39(2), pages 527-527, February.
    11. Lin, Po-Hsuan & Palfrey, Thomas R., 2024. "Cognitive hierarchies for games in extensive form," Journal of Economic Theory, Elsevier, vol. 220(C).
    12. Cardella, Eric, 2012. "Learning to make better strategic decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 382-392.
    13. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    14. Bayer, Ralph C. & Renou, Ludovic, 2016. "Logical omniscience at the laboratory," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 41-49.
    15. Paolo Crosetto & Marco Mantovani, 2018. "Representation effects in the centipede game," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-13, October.
    16. Bayer, R.-C. & Renou, Ludovic, 2016. "Logical abilities and behavior in strategic-form games," Journal of Economic Psychology, Elsevier, vol. 56(C), pages 39-59.
    17. Jeannette Brosig-Koch & Timo Heinrich & Christoph Helbach, 2012. "Exploring the Capability to Backward Induct – An Experimental Study with Children and Young Adults," Ruhr Economic Papers 0360, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    18. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.
    19. repec:zbw:rwirep:0360 is not listed on IDEAS
    20. James Tremewan & Chloé Le Coq & Alexander D. Wagner, 2013. "Social Centipedes: the Impact of Group Identity on Preferences and Reasoning," Vienna Economics Papers 1305, University of Vienna, Department of Economics.
    21. Yun Wang, 2023. "Belief and higher‐order belief in the centipede games: An experimental investigation," Pacific Economic Review, Wiley Blackwell, vol. 28(1), pages 27-73, February.

    More about this item

    Keywords

    Behavioral game theory; sequential games; strategic thinking; level-k; limited foresight.;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mib:wpaper:289. 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: Matteo Pelagatti (email available below). General contact details of provider: https://edirc.repec.org/data/dpmibit.html .

    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.