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Competitive equilibria in trading

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  • Neil A. Chriss

Abstract

This is the third paper in a series concerning the game-theoretic aspects of position-building while in competition. The first paper set forth foundations and laid out the essential goal, which is to minimize implementation costs in light of how other traders are likely to trade. The majority of results in that paper center on the two traders in competition and equilibrium results are presented. The second paper, introduces computational methods based on Fourier Series which allows the introduction of a broad range of constraints into the optimal strategies derived. The current paper returns to the unconstrained case and provides a complete solution to finding equilibrium strategies in competition and handles completely arbitrary situations. As a result we present a detailed analysis of the value (or not) of trade centralization and we show that firms who naively centralize trades do not generally benefit and sometimes, in fact, lose. On the other hand, firms that strategically centralize their trades generally will be able to benefit.

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  • Neil A. Chriss, 2024. "Competitive equilibria in trading," Papers 2410.13583, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2410.13583
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    References listed on IDEAS

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    1. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    2. Neil A. Chriss, 2024. "Position-building in competition with real-world constraints," Papers 2409.15459, arXiv.org, revised Sep 2024.
    3. 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.
    4. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    5. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    6. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Szabolcs Mike, 2006. "Market efficiency and the long-memory of supply and demand: is price impact variable and permanent or fixed and temporary?," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 107-112.
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