IDEAS home Printed from https://ideas.repec.org/p/awi/wpaper/0638.html
   My bibliography  Save this paper

Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games

Author

Listed:
  • Eichberger, Jürgen
  • Grant, Simon
  • Kelsey, David

Abstract

We propose a solution concept for a class of extensive form games with ambiguity. Specifically we consider multi-stage games. Players have CEU preferences. The associated ambiguous beliefs are revised by Generalized Bayesian Updating. We assume individuals take account of possible changes in their preferences by using consistent planning. We show that if there is ambiguity in the centipede game it is possible to sustain 'cooperation' for many periods as part of a consistent-planning equilibrium under ambiguity. In a non-cooperative bargaining game we show that ambiguity may be a cause of delay in bargaining.

Suggested Citation

  • Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2017. "Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games," Working Papers 0638, University of Heidelberg, Department of Economics.
    • Handle: RePEc:awi:wpaper:0638
    Note: This paper is part of http://archiv.ub.uni-heidelberg.de/volltextserver/view/schriftenreihen/sr-3.html
    as

    Download full text from publisher

    File URL: http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:bsz:16-heidok-233892
    File Function: Frontdoor page on HeiDOK
    Download Restriction: no
    File URL: https://archiv.ub.uni-heidelberg.de/volltextserver/23389/1/dp638.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    3. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    4. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    5. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    6. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
    7. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    8. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
    9. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    10. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.
    11. Subir Bose & Ludovic Renou, 2014. "Mechanism Design With Ambiguous Communication Devices," Econometrica, Econometric Society, vol. 82, pages 1853-1872, September.
    12. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    13. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    14. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    15. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    16. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    17. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    18. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    19. Muraviev, Igor & Riedel, Frank & Sass, Linda, 2017. "Kuhn’s Theorem for extensive form Ellsberg games," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 26-41.
    20. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 47-65.
    21. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351, September.
    22. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    23. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    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. Paolo Crosetto & Marco Mantovani, 2018. "Representation effects in the centipede game," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-13, October.
    2. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    3. Battigalli, P. & Catonini, E. & Lanzani, G. & Marinacci, M., 2019. "Ambiguity attitudes and self-confirming equilibrium in sequential games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 1-29.

    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. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    2. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    3. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    4. Jürgen Eichberger & David Kelsey, 2014. "Optimism And Pessimism In Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(2), pages 483-505, May.
    5. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    6. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    7. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    8. Gaurab Aryal & Ronald Stauber, 2014. "Trembles in extensive games with ambiguity averse players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 1-40, September.
    9. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    10. Alexander Zimper & Alexander Ludwig, 2009. "On attitude polarization under Bayesian learning with non-additive beliefs," Journal of Risk and Uncertainty, Springer, vol. 39(2), pages 181-212, October.
    11. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    12. Alexander Zimper, 2012. "The emergence of “fifty-fifty” probability judgements in a conditional Savage world," Working Papers 291, Economic Research Southern Africa.
    13. Ludwig, Alexander & Zimper, Alexander, 2014. "Biased Bayesian learning with an application to the risk-free rate puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 79-97.
    14. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    15. Frank Riedel, 2017. "Uncertain Acts in Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(4), pages 275-292, December.
    16. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    17. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    18. repec:mea:meawpa:13270 is not listed on IDEAS
    19. Eran Hanany & Peter Klibanoff & Sujoy Mukerji, 2020. "Incomplete Information Games with Ambiguity Averse Players," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 135-187, May.
    20. Dominiak, Adam & Eichberger, Jürgen & Lefort, Jean-Philippe, 2012. "Agreeable trade with optimism and pessimism," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 119-126.
    21. Xiaoyu Cheng, 2019. "Relative Maximum Likelihood Updating of Ambiguous Beliefs," Papers 1911.02678, arXiv.org, revised Oct 2021.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:awi:wpaper:0638. 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: Gabi Rauscher (email available below). General contact details of provider: https://edirc.repec.org/data/awheide.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.