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Extended Conversations in Sender-Receiver Games

Aumann and Hart (Econometrica, Nov. 2003) have shown that in games of one-sided incomplete information, the set of equilibrium outcomes achievable can be expanded considerably if the players are allowed to communicate without exogenous time limits and completely characterise the equilibria from such communication. Their research provokes (at least) four questions. (i) Is it true that the set of equilibrium payoffs stabilises (i.e. remains unchanged) if there are sufficiently many rounds of communication? (ii) Is the set of equilibria from communication which is unbounded but finite with probability one is the same as equilibria from communication which is just unbounded? (iii) Are any of these sets of equilibria "simple" and if so, is there an algorithm to compute them? (iv) Does unbounded communication (of order type w) exhaust all possibilities so that further communication is irrelevant? We show that in the context of finite Sender-Receiver games, the answer to all four is yes if the game satisfies a certain geometric condition. We then relate this condition to some geometric facts about the notion of bi-convexity and argue that if any of the questions has a negative answer then all three of the questions are likely to have a negative answer.

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Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 126.

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Length: 39
Date of creation: Sep 2004
Date of revision:
Handle: RePEc:edn:esedps:126
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  1. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
    • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
  2. Ehud Lehrer & Sylvain Sorin, 1994. "One-Shot Public Mediated Talk," Discussion Papers 1108, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. repec:cor:louvrp:-636 is not listed on IDEAS
  4. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
  5. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
  6. Blume, A. & Sobel, J., 1991. "Communication-Proof Equilibria in Cheap-Talk Games," Working Papers 91-27, University of Iowa, Department of Economics.
  7. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-98, July.
  8. Lawrence E. Blume & William R. Zame, 1993. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Game Theory and Information 9309001, EconWPA.
  9. 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.
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