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Stochastic Stability In A Double Auction

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  • Agastya, Murali
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.

Suggested Citation

  • Agastya, Murali, 2003. "Stochastic Stability In A Double Auction," Working Papers 5, University of Sydney, School of Economics.
    • Handle: RePEc:syd:wpaper:2123/7652
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    1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    2. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    3. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    4. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Noldeke, Georg & Samuelson, Larry, 1997. "A Dynamic Model of Equilibrium Selection in Signaling Markets," Journal of Economic Theory, Elsevier, vol. 73(1), pages 118-156, March.
    7. Maruta, Toshimasa, 1997. "On the Relationship between Risk-Dominance and Stochastic Stability," Games and Economic Behavior, Elsevier, vol. 19(2), pages 221-234, May.
    8. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    9. Tore Ellingsen, 1997. "The Evolution of Bargaining Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 581-602.
    10. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    11. 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.
    12. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    13. Timothy N. Cason & Daniel Friedman, 1997. "Price Formation in Single Call Markets," Econometrica, Econometric Society, vol. 65(2), pages 311-346, March.
    14. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
    15. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    16. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    17. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 363-393.
    18. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift And Equilibrium Selection," ELSE working papers 049, ESRC Centre on Economics Learning and Social Evolution.
    19. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    20. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
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    Cited by:

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    2. Klaus, Bettina & Bochet, Olivier & Walzl, Markus, 2011. "A dynamic recontracting process for multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 84-98, January.
    3. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    4. Rene Saran & Roberto Serrano, 2007. "The Evolution of Bidding Behavior in Private-Values Auctions and Double Auctions," Working Papers wp2007_0712, CEMFI.
    5. Coninx, Kristof & Deconinck, Geert & Holvoet, Tom, 2018. "Who gets my flex? An evolutionary game theory analysis of flexibility market dynamics," Applied Energy, Elsevier, vol. 218(C), pages 104-113.
    6. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    7. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.

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