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Agreeing to agree and Dutch books

Author

Listed:
  • Chen, Yi-Chun
  • Lehrer, Ehud
  • Li, Jiangtao
  • Samet, Dov
  • Shmaya, Eran

Abstract

We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsider and the agents based on the occurrence of E, such that the outsider makes positive profit in all states. We show that in a finite state space, when the agents cannot tell whether E occurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. This characterization also holds in countable state spaces with two agents. We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space with multiple agents, when each set in each agent's information partition is finite.

Suggested Citation

  • Chen, Yi-Chun & Lehrer, Ehud & Li, Jiangtao & Samet, Dov & Shmaya, Eran, 2015. "Agreeing to agree and Dutch books," Games and Economic Behavior, Elsevier, vol. 93(C), pages 108-116.
  • Handle: RePEc:eee:gamebe:v:93:y:2015:i:c:p:108-116
    DOI: 10.1016/j.geb.2015.08.002
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    References listed on IDEAS

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    1. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    2. Ng, Man-Chung, 2003. "On the duality between prior beliefs and trading demands," Journal of Economic Theory, Elsevier, vol. 109(1), pages 39-51, March.
    3. Lehrer, Ehud & Samet, Dov, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    4. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    5. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    6. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    7. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    8. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Agreement theorem; Common knowledge; Common prior; Dutch book; No trade theorem;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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