Equilibria and incentives for illiquid auction markets

ArXiv ID: 2307.15805 “View on arXiv”

Authors: Unknown

Abstract

We study a toy two-player game for periodic double auction markets to generate liquidity. The game has imperfect information, which allows us to link market spreads with signal strength. We characterize Nash equilibria in cases with or without incentives from the exchange. This enables us to derive new insights about price formation and incentives design. We show in particular that without any incentives, the market is inefficient and does not lead to any trade between market participants. We however prove that quadratic fees indexed on each players half spread leads to a transaction and we propose a quantitative value for the optimal fees that the exchange has to propose in this model to generate liquidity.

Keywords: Nash equilibria, periodic double auction, market microstructure, incentive design, Market Structure

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper introduces a game-theoretic model with Gaussian signals and derives Nash equilibria, involving advanced probability and statistics. However, it is purely theoretical with no backtesting, datasets, or code, focusing solely on analytical proofs.

  flowchart TD
    A["Research Goal:<br>Generate liquidity in<br>periodic double auctions"] --> B["Methodology: Toy 2-Player Game<br>Imperfect Information &<br>Nash Equilibrium Analysis"]
    B --> C["Simulation Inputs:<br>Signal Strength &<br>Spread Parameters"]
    C --> D{"Analysis: Nash Equilibrium<br>without incentives?"}
    D -- No --> E["Outcome: Market Inefficiency<br>No Trade Occurs"]
    D -- Yes --> F["Outcome: Trade Possible"]
    F --> G["Key Finding:<br>Quadratic fees on half-spread<br>generate liquidity"]