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The E-Mail Game Revisited — Modeling Rough Inductive Reasoning

  • UWE DULLECK

    ()

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

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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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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  1. 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.
  2. Stephen Morris, 2002. "Coordination, Communication, and Common Knowledge: A Retrospective on the Electronic-mail Game," Oxford Review of Economic Policy, Oxford University Press, vol. 18(4), pages 433-445.
  3. Dulleck, Uwe & Oechssler, Jorg, 1997. "The absent-minded centipede," Economics Letters, Elsevier, vol. 55(3), pages 309-315, September.
  4. Rubinstein, Ariel, 1995. "On the Interpretation of Decision Problems with Imperfect Recall," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 324-324, December.
  5. Stephen Morris & Hyun Song Shin, . "Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory," CARESS Working Papres 97-8, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  6. Rosemarie Nagel & Antonio Cabrales & Roc Armenter, 2002. "Equilibrium selection through incomplete information in coordination games: An experimental study," Economics Working Papers 601, Department of Economics and Business, Universitat Pompeu Fabra.
  7. 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.
  8. 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.
  9. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
  10. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, June.
  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, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  14. Aumann, Robert J. & Hart, Sergiu & Perry, Motty, 1997. "The Absent-Minded Driver," Games and Economic Behavior, Elsevier, vol. 20(1), pages 102-116, July.
  15. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  16. 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, June.
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