IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v128y2021icp125-159.html
   My bibliography  Save this article

Games in context: Equilibrium under ambiguity for belief functions

Author

Listed:
  • Dominiak, Adam
  • Eichberger, Jürgen

Abstract

We propose a new solution concept, called Context-Dependent Equilibrium Under Ambiguity (CD-EUA), for strategic games where players' beliefs may be influenced by exogenous context-related information. Players' beliefs about the strategic behavior of their opponents are represented by belief functions. The notion of belief functions allows us to combine exogenous context information in the spirit of Schelling (1960) with endogenous equilibrium beliefs about the opponents' behavior in analogy to the standard Nash equilibrium. For any finite strategic game, we prove existence of a CD-EUA for any context information and any degree of confidence in it. Moreover, we show continuity of the equilibrium correspondence. Finally, we illustrate how CD-EUA can be applied to different types of context information in games by explaining some stylized facts from experimental research on coordination.

Suggested Citation

  • Dominiak, Adam & Eichberger, Jürgen, 2021. "Games in context: Equilibrium under ambiguity for belief functions," Games and Economic Behavior, Elsevier, vol. 128(C), pages 125-159.
    • Handle: RePEc:eee:gamebe:v:128:y:2021:i:c:p:125-159
    DOI: 10.1016/j.geb.2021.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825621000415
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2021.04.002?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. Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2009. "Ambiguity and social interaction," Oxford Economic Papers, Oxford University Press, vol. 61(2), pages 355-379, April.
    2. Roger B. Myerson, 2009. "Learning from Schelling's Strategy of Conflict," Journal of Economic Literature, American Economic Association, vol. 47(4), pages 1109-1125, December.
    3. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    5. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    6. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    7. , & ,, 2012. "Forward induction reasoning revisited," Theoretical Economics, Econometric Society, vol. 7(1), January.
    8. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, December.
    9. Dufwenberg, Martin & Gächter, Simon & Hennig-Schmidt, Heike, 2011. "The framing of games and the psychology of play," Games and Economic Behavior, Elsevier, vol. 73(2), pages 459-478.
    10. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    11. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    12. 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.
    13. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    14. Roberto A. Weber, 2006. "Managing Growth to Achieve Efficient Coordination in Large Groups," American Economic Review, American Economic Association, vol. 96(1), pages 114-126, March.
    15. Amanda Friedenberg & Martin Meier, 2017. "The context of the game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 347-386, February.
    16. Chakravarty, Surajeet & Fonseca, Miguel A. & Kaplan, Todd R., 2014. "An experiment on the causes of bank run contagions," European Economic Review, Elsevier, vol. 72(C), pages 39-51.
    17. 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.
    18. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016064, October.
    19. Jürgen Eichberger & David Kelsey & Burkhard Schipper, 2008. "Granny Versus Game Theorist: Ambiguity in Experimental Games," Theory and Decision, Springer, vol. 64(2), pages 333-362, March.
    20. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    21. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107627314, October.
    22. Jürgen Eichberger & Ani Guerdjikova, 2018. "Do markets prove pessimists right ?," Post-Print hal-01869548, HAL.
    23. 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, pages 483-505, May.
    24. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016040, October.
    25. P. Battigalli & S. Cerreia‐Vioglio & F. Maccheroni & M. Marinacci, 2016. "A Note on Comparative Ambiguity Aversion and Justifiability," Econometrica, Econometric Society, vol. 84, pages 1903-1916, September.
    26. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    27. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    28. Martin Brown & Stefan T. Trautmann & Razvan Vlahu, 2017. "Understanding Bank-Run Contagion," Management Science, INFORMS, vol. 63(7), pages 2272-2282, July.
    29. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    30. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107638105, October.
    31. Jean-Yves Jaffray & Fabrice Philippe, 1997. "On the Existence of Subjective Upper and Lower Probabilities," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 165-185, February.
    32. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    33. repec:spr:thdchp:978-3-540-68437-4_12 is not listed on IDEAS
    34. Wakker, Peter P., 2005. "Decision-foundations for properties of nonadditive measures: general state spaces or general outcome spaces," Games and Economic Behavior, Elsevier, vol. 50(1), pages 107-125, January.
    35. Jürgen Eichberger & David Kelsey, 2004. "Sequential Two-Player Games With Ambiguity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1229-1261, November.
    36. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016057, October.
    37. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    38. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    39. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    40. Ronald Stauber, 2019. "A strategic product for belief functions," ANU Working Papers in Economics and Econometrics 2019-668, Australian National University, College of Business and Economics, School of Economics.
    41. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107674165, October.
    42. Eichberger, Jurgen & Kelsey, David, 2002. "Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 436-466, October.
    43. Jürgen Eichberger & Ani Guerdjikova, 2018. "Do Markets Prove Pessimists Right?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 2259-2295, November.
    44. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    45. 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.
    46. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    47. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    48. repec:dau:papers:123456789/157 is not listed on IDEAS
    49. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    50. Stauber, Ronald, 2019. "A strategic product for belief functions," Games and Economic Behavior, Elsevier, vol. 116(C), pages 38-64.
    51. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    52. Jaffray, Jean-Yves & Wakker, Peter, 1993. "Decision Making with Belief Functions: Compatibility and Incompatibility with the Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 255-271, December.
    53. Wakker, Peter, 1990. "Characterizing optimism and pessimism directly through comonotonicity," Journal of Economic Theory, Elsevier, vol. 52(2), pages 453-463, December.
    54. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    55. 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. Péter Bayer & Ani Guerdjikova, 2020. "Optimism leads to optimality: Ambiguity in network formation," Working Papers hal-03005107, HAL.
    2. Adam Dominiak & Ani Guerdjikova, 2021. "Special Issue on Ambiguity and Strategic Interactions in Honor of Jürgen Eichberger," Theory and Decision, Springer, vol. 90(3), pages 301-307, May.
    3. Johanna Etner & Meglena Jeleva & Olivier Renault, 2024. "Dynamic decision-making when ambiguity attitudes depend on exogenous events," Theory and Decision, Springer, vol. 96(2), pages 269-295, March.

    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. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    3. Yang, Jian, 2018. "Game-theoretic modeling of players’ ambiguities on external factors," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 31-56.
    4. Jian Yang, 2015. "Game-theoretic Modeling of Players' Ambiguities on External Factors," Papers 1510.06812, arXiv.org, revised Apr 2017.
    5. 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.
    6. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    7. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    8. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    9. Dominiak, Adam & Duersch, Peter, 2015. "Benevolent and Malevolent Ellsberg Games," Working Papers 0592, University of Heidelberg, Department of Economics.
    10. Péter Bayer & Ani Guerdjikova, 2020. "Optimism leads to optimality: Ambiguity in network formation," Working Papers hal-03005107, HAL.
    11. Loïc Berger & Louis Eeckhoudt, 2021. "Risk, Ambiguity, and the Value of Diversification," Management Science, INFORMS, vol. 67(3), pages 1639-1647, March.
    12. Florian H. Schneider & Martin Schonger, 2019. "An Experimental Test of the Anscombe–Aumann Monotonicity Axiom," Management Science, INFORMS, vol. 65(4), pages 1667-1677, April.
    13. De Marco, Giuseppe & Romaniello, Maria, 2013. "A limit theorem for equilibria under ambiguous belief correspondences," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 431-438.
    14. 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.
    15. Takashi Ui, 2021. "Strategic Ambiguity in Global Games," Working Papers on Central Bank Communication 032, University of Tokyo, Graduate School of Economics.
    16. Driouchi, Tarik & Trigeorgis, Lenos & So, Raymond H.Y., 2020. "Individual antecedents of real options appraisal: The role of national culture and ambiguity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1018-1032.
    17. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Sonderforschungsbereich 504 Publications 07-50, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
      • Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Papers 07-50, Sonderforschungsbreich 504.
    18. Loïc Berger & Louis Eeckhoudt, 2020. "Risk, Ambiguity, And The Value Of Diversification," Working Papers hal-02910906, HAL.
    19. repec:awi:wpaper:0448 is not listed on IDEAS
    20. Evan M. Calford & Gregory DeAngelo, 2023. "Ambiguity and enforcement," Experimental Economics, Springer;Economic Science Association, vol. 26(2), pages 304-338, April.
    21. Han Bleichrodt & Christophe Courbage & Béatrice Rey, 2019. "The value of a statistical life under changes in ambiguity," Journal of Risk and Uncertainty, Springer, vol. 58(1), pages 1-15, February.

    More about this item

    Keywords

    Strategic games; Context information; Non-additive beliefs; Belief functions; Choquet expected utility; Equilibrium under ambiguity; Optimism and pessimism;
    All these keywords.

    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:eee:gamebe:v:128:y:2021:i:c:p:125-159. 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/622836 .

    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.