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Stochastic Stability In A Double Auction

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  • Agastya, Murali
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    Abstract

    In a k-double auction, a buyer and a seller must simultaneously announce a bid and an ask price respectively. Exchange of the indivisible good takes place if and only if the bid is at least as high as the ask, the trading price being the bid price with probability k and the ask price with probability (1 - k). We show that the stable equilibria of a complete information k-double approximate an asymmetric Nash Bargaining solution with the seller's bargaining power decreasing in k. Note that ceteras paribus, the payoffs of the seller of the one-shot game increase in k. Nevertheless, as the stochastically stable equilibrium price decreases in k, choosing the seller's favourite price with a relatively higher probability in individual encounters makes him worse off in the long run.

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    File URL: http://hdl.handle.net/2123/7652
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    Bibliographic Info

    Paper provided by University of Sydney, School of Economics in its series Working Papers with number 5.

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    Date of creation: May 2003
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    Handle: RePEc:syd:wpaper:2123/7652

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    Postal: Sydney, NSW 2006
    Phone: 61 +2 9351 5055
    Fax: 61 +2 9351 4341
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    Web page: http://sydney.edu.au/arts/economics
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    Related research

    Keywords: k-double auction; multiple equilibria; risk potential; stochastic stability; Nash Bargaining Solution;

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    1. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
    2. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
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    9. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    10. Gerorg N´┐Żldeke & Larry Samuelson, . "A Dynamic Model of Equilibrium Selection In Signaling Markets," ELSE working papers 038, ESRC Centre on Economics Learning and Social Evolution.
    11. Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    13. S. Morris & R. Rob & H. Shin, 2010. "p-dominance and Belief Potential," Levine's Working Paper Archive 505, David K. Levine.
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