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Geanakoplos and Sebenius model with noise

Author

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  • Doron Sonsino

    (Technion, Israel Institute of Technology, Haifa 32000, Israel)

Abstract

Assume that two risk neutral agents with asymmetric information simultaneously expect a gain from zero-sum betting. Geanakoplos and Sebenius (1983) (henceforth GS) consider the case where the agents may re-evaluate the profitability of betting successively before the payments are realized. They prove that one of the players must reject the proposed bet within some finite number $(N_0)$ of re-evaluation rounds. This paper extends the GS model to the case where there exists a small probability that players accept the bet when they should reject it. We claim that, generically, the GS results are not effected by small noise. That is, when is low, the players will reject the bet within $N_0$ iterations with probability close to one. Surprisingly, we find a non-generic example where - for every positive - the agents keep expecting a gain from betting forever. Our main Theorem, however, says that even when the noise is large and even in such non generic examples one of the following two alternatives must hold: (A) Some agent expects a loss from betting (and thus rejects the bet with high probability) after some finite number of re-evaluation rounds, or (B) The expected gain from betting goes to zero for both agents. Moreover, if there is a small cost to entertaining the bet, then some player must expect a loss from betting eventually.

Suggested Citation

  • Doron Sonsino, 1998. "Geanakoplos and Sebenius model with noise," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 111-130.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:1:p:111-130
    Note: Received February 1996/Revised version August 1996/Final version March 1997
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    Cited by:

    1. Ido Erev & Sharon Gilat-Yihyie & Davide Marchiori & Doron Sonsino, 2015. "On loss aversion, level-1 reasoning, and betting," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 113-133, February.
    2. Angrisani Marco & Guarino Antonio & Huck Steffen & Larson Nathan C, 2011. "No-Trade in the Laboratory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-58, April.

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