Common Information Approach for Static Team Problems with Polish Spaces and Existence of Optimal Policies

TL;DR

This paper extends the common information approach to static team problems with Polish spaces, proving the existence of optimal strategies in a continuous setting by developing an appropriate policy topology.

Contribution

It generalizes the common information method from discrete to continuous spaces, establishing existence results for team-optimal strategies under shared observations.

Findings

Existence of team-optimal strategies proven for static teams with Polish spaces.

Conversion of team problems into centralized stochastic control problems.

Development of a suitable topology on policies for continuous spaces.

Abstract

In this paper, we demonstrate the existence of team-optimal strategies for static teams under observation-sharing information structures. Assuming that agents can access shared observations, we begin by converting the team problem into an equivalent centralized stochastic control problem through the introduction of a topology on policies. We subsequently apply conventional methods from stochastic control to prove the existence of team-optimal strategies. This study expands upon the widely recognized common information approach for team problems, originally designed for discrete scenarios, and adapts it to a more abstract continuous framework. The primary difficulty in this context is to establish the appropriate topology on policies.