A Game of Competition for Risk

ArXiv ID: 2305.18941 “View on arXiv”

Authors: Unknown

Abstract

In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence and uniqueness of a Nash equilibrium and providing an analytical solution. We then extend this analysis to multi-player scenarios, introducing a new numerical algorithm for its calculation. A key novelty of our work lies in using regret minimization algorithms to solve continuous games through discretization. This groundbreaking approach enables us to incorporate additional real-world factors like market frictions and risk correlations among firms. We also experimentally validate that the Nash equilibrium in our model also serves as a correlated equilibrium. Our findings illuminate how market frictions and risk correlations affect strategic risk-taking. We also explore how policy measures can impact risk-taking and its associated rewards, with our model providing broader applicability than the Diamond-Dybvig framework. We make our methodology and open-source code available at https://github.com/louisabraham/cfrgame Finally, we contribute methodologically by advocating the use of algorithms in economics, shifting focus from finite games to games with continuous action sets. Our study provides a solid framework for analyzing strategic interactions in continuous action games, emphasizing the importance of market frictions, risk correlations, and policy measures in strategic risk-taking dynamics.

Keywords: Game Theory, Nash Equilibrium, Regret Minimization, Market Frictions, Risk Correlations

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced continuous game theory, Nash equilibrium proofs, and regret minimization algorithms (like counterfactual regret minimization), indicating high mathematical complexity. It also features a strong empirical component with open-source code, experimental validation of equilibria, and concrete simulations of market frictions and risk correlations, making it backtest-ready and implementation-heavy.

  flowchart TD
    A["Research Goal:<br>Model Strategic Risk-Taking"] --> B["Method: Two-Player<br>Normal Form Game"]
    B --> C["Input: Continuous Action Space"]
    C --> D{"Find Nash Equilibrium"}
    D -- Analytical Solution --> E["Output: Unique Nash Equilibrium<br>Validated as Correlated Equilibrium"]
    D -- Numerical Algorithm --> F["Method: Multi-Player<br>Regret Minimization"]
    F --> G["Input: Market Frictions &<br>Risk Correlations"]
    G --> H["Outcome: Insights on<br>Policy Measures &<br>Risk Dynamics"]