Martingale theory for Dynkin games with asymmetric information

2025-10-17

AI Summary

This paper investigates necessary and sufficient conditions for random stopping times to constitute a saddle point in zero-sum Dynkin games under non-Markovian settings with partial or asymmetric information. Methodologically, it introduces— for the first time—the equilibrium payoff as a pair of upper and lower semimartingales, and establishes an exact correspondence between stopping-time strategies and equilibrium properties via their Doob–Meyer decompositions; integrating martingale theory, stochastic analysis, and game theory, it develops an equilibrium identification mechanism applicable to general filtrations. The main contributions are: (i) the first universal existence criterion for saddle points in such games; (ii) a complete characterization of the dynamic structure of equilibrium strategies under asymmetric information; and (iii) novel theoretical tools and an analytical framework for dynamic games with incomplete information.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization

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.

Problem

• Characterizing saddle points in asymmetric information Dynkin games
• Establishing necessary and sufficient conditions for randomized stopping times
• Developing martingale methodology for general non-Markovian information structures

Innovation

• Randomized stopping times for asymmetric information games
• Non-Markovian framework with universal information structure
• Saddle point strategies via Doob-Meyer decomposition dynamics