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Unmediated communication in repeated games with imperfect monitoring

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  • Urbano, A.
  • Vila, J. E.

Abstract

We show that any correlated equilibrium payoff of two-player repeated games with imperfect monitoring and without discounting can be reached as the Nash equilibrium payoff of the game extended by a universal mechanism of unmediated communication. This result holds regardless the particular concept of equlibrium involved (upper, lower, Banach or uniform equlibrium). The communication mechanism is built up by using commutative one-way functions. These functions are designed with the help of cryptographic tools.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 46 (2004)
Issue (Month): 1 (January)
Pages: 143-173

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Handle: RePEc:eee:gamebe:v:46:y:2004:i:1:p:143-173

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
  2. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  3. Forges, F., 1984. "An approach to communication equilibria," CORE Discussion Papers 1984035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. FORGES, Françoise, . "Universal mechanisms," CORE Discussion Papers RP -914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  6. Gossner, O., 1999. "Repeated Games played by Cryptographically Sophesticated Players," Papers 99-07, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  7. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer, vol. 20(3), pages 211-26.
  8. Farrell, Joseph, 1988. "Communication, coordination and Nash equilibrium," Economics Letters, Elsevier, vol. 27(3), pages 209-214.
  9. Rubinstein, Ariel & Yaari, Menahem E., 1983. "Repeated insurance contracts and moral hazard," Journal of Economic Theory, Elsevier, vol. 30(1), pages 74-97, June.
  10. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer, vol. 19(2), pages 191-217.
  11. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
  12. repec:fth:louvco:9856 is not listed on IDEAS
  13. repec:fth:louvco:9836 is not listed on IDEAS
  14. Amparo Urbano & Jose E. Vila, 2002. "Computational Complexity and Communication: Coordination in Two-Player Games," Econometrica, Econometric Society, vol. 70(5), pages 1893-1927, September.
  15. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
  16. Steven A. Matthews & Andrew Postlewaite, 1987. "Pre-Play Communication in Two-Person Sealed-Bid Double Auctions," Discussion Papers 744R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. Ehud Lehrer & Sylvain Sorin, 1994. "One-Shot Public Mediated Talk," Discussion Papers 1108, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  19. Futia, Carl, 1977. "The complexity of economic decision rules," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 289-299, December.
  20. Radner, Roy, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 43-57, January.
  21. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer, vol. 25(2), pages 177-88.
  22. Joseph Farrell & Matthew Rabin, 1996. "Cheap Talk," Journal of Economic Perspectives, American Economic Association, vol. 10(3), pages 103-118, Summer.
  23. Ben-Porath, Elchanan & Kahneman, Michael, 1996. "Communication in Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 70(2), pages 281-297, August.
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Citations

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Cited by:
  1. O. Gossner, 1999. "Repeated games played by cryptographically sophisticated players," THEMA Working Papers 99-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  2. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics.
  3. O. Gossner, 2000. "Sharing a long secret in a few public words," THEMA Working Papers 2000-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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