Paper: arXiv 2311.01086

Abstract

In this paper, we study a non-zero-sum game with two players, where each of the players plays what we call Bermudan strategies and optimizes a general non-linear assessment functional of the pay-off. By using a recursive construction, we show that the game has a Nash equilibrium point.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly abstract, theoretical stochastic game framework with advanced tools like backward stochastic differential equations and nonlinear risk measures, but contains no empirical data, code, or backtesting results.

Research Flowchart

  flowchart TD
  A["Research Goal: Find Nash Equilibrium in<br>Non-Zero-Sum Dynkin Games with<br>Bermudan Strategies & Non-Linear Payoffs"] --> B["Methodology: Recursive Construction"]
  B --> C["Input: General Non-Linear<br>Assessment Functionals"]
  C --> D["Computational Process:<br>Value Iteration &<br>Fixed Point Analysis"]
  D --> E["Outcome: Proven Existence<br>of Nash Equilibrium"]
  E --> F["Application: Pricing<br>Derivatives/Contingent Claims"]