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Insider trading in discrete time Kyle games

Author

Listed:
  • Christoph Kühn

    (Goethe University Frankfurt)

  • Christopher Lorenz

    (Goethe University Frankfurt)

Abstract

We present a new discrete time version of Kyle’s (Econometrica 53(6):1315–1335, 1985) classic model of insider trading, formulated as a generalised extensive form game. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise expected profits while the market maker observes the total order flow and sets prices accordingly. First, we show how the multi-period model with finitely many pure strategies can be reduced to a (static) social system in the sense of Debreu (Proc Natl Acad Sci 38(10):886–893, 1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (Econometrica 50(4):863–894, 1982). This works for any probability distribution with finite support of the noise trader’s demand and the true value, and for any finite information flow of the insider. In contrast to Kyle (1985) with normal distributions, equilibria exist in general only in mixed strategies and not in pure strategies. In the single-period model we establish bounds for the insider’s strategy in equilibrium. Finally, we prove the existence of an equilibrium for the game with a continuum of actions, by considering an approximating sequence of games with finitely many actions. Because of the lack of compactness of the set of measurable price functions, standard infinite-dimensional fixed point theorems are not applicable.

Suggested Citation

  • Christoph Kühn & Christopher Lorenz, 2025. "Insider trading in discrete time Kyle games," Mathematics and Financial Economics, Springer, volume 19, number 2, December.
  • Handle: RePEc:spr:mathfi:v:19:y:2025:i:1:d:10.1007_s11579-024-00376-w
    DOI: 10.1007/s11579-024-00376-w
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    More about this item

    Keywords

    Information asymmetry; Kyle model; Extensive form game; Sequential equilibrium; Komlós’ theorem;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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