Paper: arXiv 2510.15616

Authors: Tiziano De Angelis, Jan Palczewski, Jacob Smith

Abstract

This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and covers essentially any information structure. Our methodology relies on the identification of suitable super and submartingales involving players’ equilibrium payoffs. Saddle point strategies are characterised in terms of the dynamics of those equilibrium payoffs and are related to their Doob-Meyer decompositions.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a breakthrough pure mathematical framework for non-Markovian Dynkin games under asymmetric information using advanced martingale theory and Doob-Meyer decompositions. While it is purely theoretical with no empirical backtesting or real-world dataset applications, it solves a long-standing theoretical bottleneck in game theory and optimal stopping.

Research Flowchart

  flowchart TD
    A[Research Goal: Characterize Saddle Point Equilibria in Non-Markovian Dynkin Games with Asymmetric Information] --> B[Inputs: Non-Markovian Framework, Arbitrary Information Structures, & Randomised Stopping Times]
    B --> C[Methodology: Construct Super/Submartingale Models for Players' Equilibrium Payoffs]
    C --> D[Analysis: Apply Doob-Meyer Decomposition to Payoff Dynamics]
    D --> E[Outcomes: Necessary and Sufficient Conditions for Saddle Points in Asymmetric Dynkin Games]