On a continuous time game with incomplete information

TL;DR

This paper studies zero-sum continuous-time games with incomplete information, showing how the informed player's optimal strategy can be derived via an auxiliary optimization over martingale measures, with explicit solutions in specific cases.

Contribution

It introduces a method to compute the informed player's optimal strategy using an auxiliary optimization problem over martingale measures, providing explicit characterizations.

Findings

Optimal strategies can be derived through an auxiliary martingale measure optimization.

Explicit solutions are obtained in several example scenarios.

The approach offers a new way to analyze incomplete information games.

Abstract

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some martingale measures. One also characterizes the optimal martingale measures and compute it explicitely in several examples.