Insider trading in discrete time Kyle games

ArXiv ID: 2312.00904 “View on arXiv”

Authors: Unknown

Abstract

We present a new discrete time version of Kyle’s (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 (1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (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.

Keywords: Kyle Model, Insider Trading, Market Microstructure, Game Theory, Equilibrium Analysis, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematical, focusing on proving existence of equilibria in a discrete-time Kyle model using game theory, fixed-point theorems, and measure theory, with no empirical data, backtests, or implementation details.

  flowchart TD
    A["Research Goal:<br>Discrete-time Kyle Model<br>Equilibrium Analysis"] --> B["Methodology:<br>Generalised Extensive Form Game<br>Reduction to Debreu Social System"]
    B --> C["Key Setting:<br>Insider, Noise Traders, Market Maker<br>Finite Support Distributions"]
    C --> D["Computational Process:<br>Kreps-Wilson Existence Proof<br>Approximation Sequence for Continuum"]
    D --> E["Key Finding 1:<br>Equilibrium Exists in Mixed Strategies<br>Pure Strategies Not Guaranteed"]
    E --> F["Key Finding 2:<br>Equilibrium Bounds Established for<br>Single-Period Model"]
    F --> G["Key Finding 3:<br>Continuum of Actions Equilibrium Proven<br>via Finite-Action Approximation"]