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Stochastic Stability In A Double Auction

  • Agastya, Murali
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    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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    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
    Contact details of provider: Postal: Sydney, NSW 2006
    Phone: 61 +2 9351 5055
    Fax: 61 +2 9351 4341
    Web page: http://sydney.edu.au/arts/economics
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    1. Ellingsen, Tore, 1995. "The Evolution of Bargaining Behavior," SSE/EFI Working Paper Series in Economics and Finance 61, Stockholm School of Economics.
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    6. Timothy N. Cason & Daniel Friedman, 1997. "Price Formation in Single Call Markets," Econometrica, Econometric Society, vol. 65(2), pages 311-346, March.
    7. 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.
    8. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    9. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    10. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
    11. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    12. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    13. Troger, Thomas, 2002. "Why Sunk Costs Matter for Bargaining Outcomes: An Evolutionary Approach," Journal of Economic Theory, Elsevier, vol. 102(2), pages 375-402, February.
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