Team and Person-by-Person Optimality Conditions of Differential Decision Systems

TL;DR

This paper establishes necessary and sufficient optimality conditions for distributed differential decision systems with decentralized information, using Hamiltonian systems and convexity assumptions.

Contribution

It derives novel team and person-by-person optimality conditions for systems with decentralized information structures, including sufficiency under convexity.

Findings

Necessary conditions expressed via Hamiltonian systems

Sufficient conditions under convexity assumptions

Applicable to distributed decision systems with decentralized info

Abstract

In this paper, we derive team and person-by-person optimality conditions for distributed differential decision systems with different or decentralized information structures. The necessary conditions of optimality are given in terms of Hamiltonian system of equations consisting of a coupled backward and forward differential equations and a Hamiltonian projected onto the subspace generated by the decentralized information structures. Under certain global convexity conditions it is shown that the optimality conitions are also sufficient.