A BSDE approach to stochastic differential games with incomplete information

TL;DR

This paper models a two-player zero-sum stochastic differential game with asymmetric information, using a BSDE framework to quantify the informed player's strategic information revelation.

Contribution

It introduces a novel BSDE-based approach to analyze the impact of private information in stochastic differential games.

Findings

Value function expressed via a minimization over martingale measures.

Reformulation of the game as a BSDE-driven optimization problem.

Quantification of information revelation needed for optimal play.

Abstract

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our aim is to quantify the amount of information the informed player has to reveal in order to play optimally: to do so, we show that the value function of this zero-sum game can be rewritten as a minimization problem over some martingale measures with a payoff given by the solution of a backward stochastic differential equation.