Competitive equilibria in trading

ArXiv ID: 2410.13583 “View on arXiv”

Authors: Unknown

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.

Keywords: Game Theory, Position Building, Equilibrium Strategies, Trade Centralization, Implementation Costs, Equities / Market Microstructure

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, relying on Nash equilibrium concepts, closed-form solutions for multi-trader competition, and market impact modeling, which indicates dense mathematical analysis. However, the excerpt focuses entirely on theoretical models and strategic implications without any mention of backtesting, specific datasets, or empirical validation of the strategies.

  flowchart TD
    A["Research Goal: Find equilibrium strategies for competing traders"] --> B["Method: Game-theoretic analysis"]
    B --> C["Model: N traders competing on position building"]
    C --> D{"Centralization?"}
    D -- Naive --> E["Outcome: No benefit, often losses"]
    D -- Strategic --> F["Outcome: Potential gains"]
    E --> G["Key Finding: Centralization requires strategy, not just scale"]
    F --> G