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The E-Mail Game Revisited — Modeling Rough Inductive Reasoning

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  • UWE DULLECK

    ()
    (School of Economics and Finance, Queensland University of Technology, GPO Box 2434, Brisbane QLD 4001, Australia)

Abstract

I study the robustness of Rubinstein's (1989) E-Mail Game results by varying the information that players can utilize. The article follows one of Morris' (2002) reactions to the E-Mail game "that one should try to come up with a model of boundedly rational behavior that delivers predictions that are insensitive to whether there is common knowledge or a large number of levels of knowledge". Players in my model are presumed to use 'rough inductive reasoning' because they cannot utilize exact information.The information structure in the E-Mail game is generalized and the conditions are characterized under which Rubinstein's results hold. I find that rough inductive reasoning generates a payoff dominant equilibrium where the expected payoffs change continuously (instead of discretely) in the probability of "faulty" communication.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 09 (2007)
Issue (Month): 02 ()
Pages: 323-339

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Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:02:p:323-339

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Related research

Keywords: Inductive reasoning; JEL-Classification: C72;

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References

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  1. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  2. Stephen Morris & Hyun Song Shin, . "Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory," Penn CARESS Working Papers 72042421d029130510780dde2, Penn Economics Department.
  3. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  4. Binmore, Ken & Samuelson, Larry, 2001. "Coordinated Action in the Electronic Mail Game," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 6-30, April.
  5. 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.
  6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  7. Antonio Cabrales & Rosemarie Nagel & Roc Armenter, 2007. "Equilibrium selection through incomplete information in coordination games: an experimental study," Experimental Economics, Springer, vol. 10(3), pages 221-234, September.
  8. Atsushi Kajii & Stephen Morris, 1997. "Payoff Continuity in Incomplete Information Games," Discussion Papers 1193R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, December.
  10. Aumann, Robert J. & Hart, Sergiu & Perry, Motty, 1997. "The Absent-Minded Driver," Games and Economic Behavior, Elsevier, vol. 20(1), pages 102-116, July.
  11. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  12. Morris Stephen E, 2002. "Faulty Communication: Some Variations on the Electronic Mail Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-26, January.
  13. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  14. U. Dulleck & J. Oechssler, 1996. "The Absent-Minded Centipede," SFB 373 Discussion Papers 1996,98, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  15. Stephen Morris, 2004. "Coordination, Communication and Common Knowledge: A Retrospective on the Electronic Mail Game," Yale School of Management Working Papers ysm340, Yale School of Management.
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Cited by:
  1. Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient spaces of boundedly rational types," Economics Working Papers 1287, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Koji Takamiya & Akira Tanaka, 2006. "Mutual Knowledge of Rationality in the Electronic Mail Game," ISER Discussion Paper 0650, Institute of Social and Economic Research, Osaka University.

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