Continuous-time limit of dynamic games with incomplete information and a more informed player

TL;DR

This paper investigates the continuous-time limit of a two-player zero-sum dynamic game with asymmetric information, characterizing the limit value via an auxiliary problem and a Hamilton-Jacobi equation.

Contribution

It introduces a novel analysis of the limit value in dynamic games with incomplete information, using viscosity solutions of Hamilton-Jacobi equations.

Findings

Existence of a limit value as stage frequency increases.

Characterization of the limit value through an auxiliary optimization problem.

Solution of a second order Hamilton-Jacobi equation with convexity constraints.

Abstract

We study a two-player, zero-sum, dynamic game with incomplete information where one of the players is more informed than his opponent. We analyze the limit value as the players play more and more frequently. The more informed player observes the realization of a Markov process (X,Y) on which the payoffs depend, while the less informed player only observes Y and his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages goes to zero. This value is characterized through an auxiliary optimization problem and as the unique viscosity solution of a second order Hamilton-Jacobi equation with convexity constraints.