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Robustness of equilibrium in the Kyle model of informed speculation

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  • Alex Boulatov
  • Dan Bernhardt

Abstract

We analyze a static Kyle (Continuous auctions and insider trading. Princeton University, Princeton, 1983 ) model in which a risk-neutral informed trader can use arbitrary (linear or non-linear) deterministic strategies, and a finite number of market makers can use arbitrary pricing rules. We establish a strong sense in which the linear Kyle equilibrium is robust: the first variation in any agent’s expected payoff with respect to a small variation in his conjecture about the strategies of others vanishes at equilibrium. Thus, small errors in a market maker’s beliefs about the informed speculator’s trading strategy do not reduce his expected payoffs. Therefore, the original equilibrium strategies remain optimal and still constitute an equilibrium (neglecting the higher-order terms). We also establish that if a non-linear equilibrium exists, then it is not robust. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Alex Boulatov & Dan Bernhardt, 2015. "Robustness of equilibrium in the Kyle model of informed speculation," Annals of Finance, Springer, vol. 11(3), pages 297-318, November.
    • Handle: RePEc:kap:annfin:v:11:y:2015:i:3:p:297-318
    DOI: 10.1007/s10436-015-0264-2
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    References listed on IDEAS

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    1. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    2. Barelli, Paulo, 2009. "Consistency of beliefs and epistemic conditions for Nash and correlated equilibria," Games and Economic Behavior, Elsevier, vol. 67(2), pages 363-375, November.
    3. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
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    Citations

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    Cited by:

    1. Umut Çetin & Kasper Larsen, 2024. "Is Kyle’s equilibrium model stable?," Mathematics and Financial Economics, Springer, volume 18, number 3, February.
    2. Cécile Bastidon, 2017. "Stock markets fragmentation, volatility and final investors," Annals of Finance, Springer, vol. 13(4), pages 435-451, November.
    3. Umut Cetin & Kasper Larsen, 2023. "Is Kyle's equilibrium model stable?," Papers 2307.09392, arXiv.org, revised Jul 2023.
    4. Charles-Albert Lehalle & Eyal Neuman & Segev Shlomov, 2021. "Phase Transitions in Kyle's Model with Market Maker Profit Incentives," Papers 2103.04481, arXiv.org.

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    More about this item

    Keywords

    Market microstructure; Informed speculation; Bayesian Nash equilibrium; Uniqueness; Robustness; Information; G12; G14; C62;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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