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Position building in competition is a game with incomplete information

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  • Neil A. Chriss

Abstract

This paper examines strategic trading under incomplete information, where firms lack full knowledge of key aspects of their competitors' trading strategies such as target sizes and market impact models. We extend previous work on competitive trading equilibria by incorporating uncertainty through the framework of Bayesian games. This allows us to analyze scenarios where firms have diverse beliefs about market conditions and each other's strategies. We derive optimal trading strategies in this setting and demonstrate how uncertainty significantly impacts these strategies compared to the complete information case. Furthermore, we introduce a novel approach to model the presence of non-strategic traders, even when strategic firms disagree on their characteristics. Our analysis reveals the complex interplay of beliefs and strategic adjustments required in such an environment. Finally, we discuss limitations of the current model, including the reliance on linear market impact and the lack of dynamic strategy adjustments, outlining directions for future research.

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  • Neil A. Chriss, 2025. "Position building in competition is a game with incomplete information," Papers 2501.01241, arXiv.org.
    • Handle: RePEc:arx:papers:2501.01241
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    References listed on IDEAS

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    1. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    2. Neil A. Chriss, 2024. "Optimal position-building strategies in competition," Papers 2409.03586, arXiv.org, revised Nov 2024.
    3. Roger B. Myerson, 2004. "Comments on "Games with Incomplete Information Played by 'Bayesian' Players, I--III Harsanyi's Games with Incoplete Information"," Management Science, INFORMS, vol. 50(12_supple), pages 1818-1824, December.
    4. Neil A. Chriss, 2024. "Competitive equilibria in trading," Papers 2410.13583, arXiv.org, revised Oct 2024.
    5. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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