Position building in competition is a game with incomplete information

ArXiv ID: 2501.01241 “View on arXiv”

Authors: Unknown

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.

Keywords: Bayesian games, strategic trading, market impact, game theory, incomplete information, equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, relying heavily on game theory, Bayesian Nash equilibrium derivations, and complex analytical proofs, placing it in the ‘Lab Rats’ category where high theory outweighs empirical testing.

  flowchart TD
    A["Research Goal: How does incomplete information<br>affect optimal trading strategies?"]
    
    B["Methodology: Bayesian Games Framework<br>Uncertainty on competitor trading parameters"]
    
    C["Inputs: Beliefs about<br>Target Sizes & Market Impact<br>Presence of Non-Strategic Traders"]
    
    D["Computation: Derivation of Optimal<br>Bayesian Nash Equilibrium Strategies"]
    
    E["Outcomes: Equilibrium Analysis<br>& Comparison to Complete Info Case"]
    
    F["Key Findings:<br>1. Uncertainty alters optimal strategies significantly<br>2. Complex interplay of beliefs & adjustments<br>3. Limitations: Linear impact, static strategies"]
    
    A --> B
    B --> C
    C --> D
    D --> E
    E --> F