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Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence

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  • Marina Sandomirskaia

    (Center for Market Studies and Spatial Economics, National Research University Higher School of Economics, 20 Myasnitskaya st., Moscow 101000, Russia)

Abstract

We consider the repeated zero-sum bidding game with incomplete information on one side with non-normalized total payoff. De Meyer and Marino [(2005) Continuous versus discrete market game, Cowles Foundation Discussion Paper 1535] and Domansky and Kreps [(2005) Repeated games with asymmetric information and random price fluctuations at finance markets, Proc. Appl. Ind. Math. 12(4), 950–952 (in Russian)] investigated a game Gn modeling multistage bidding with asymmetrically informed agents and proved that for this game Vn converges to a finite limit V∞, i.e., the error term is O(1). In this paper, we show that for this example Vn converges to the limit exponentially fast. For this purpose we apply the optimal strategy σ∞ of insider in the infinite-stage game obtained by Domansky [(2007) Repeated games with asymmetric information and random price fluctuations at finance markets, Int. J. Game Theor. 36(2), 241–257] to the n-stage game and deduce that it is εn-optimal with εn exponentially small.

Suggested Citation

  • Marina Sandomirskaia, 2017. "Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-7, March.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:01:n:s0219198916500171
    DOI: 10.1142/S0219198916500171
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    References listed on IDEAS

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    1. Hadiza Moussa Saley & Bernard De Meyer, 2003. "On the strategic origin of Brownian motion in finance," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 285-319.
    2. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 241-257, October.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    4. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
    5. Bernard de Meyer & Hadiza Moussa Saley, 2003. "On the strategic origin of Brownian motion in Finance," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00259737, HAL.
    6. Bernard de Meyer & Hadiza Moussa Saley, 2003. "On the strategic origin of Brownian motion in Finance," Post-Print hal-00259737, HAL.
    7. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 5, pages 109-154, Elsevier.
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    Cited by:

    1. Fedor Sandomirskiy, 2018. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," Dynamic Games and Applications, Springer, vol. 8(1), pages 180-198, March.

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