Optimal Symmetric Strategies in Multi-Agent Systems with Decentralized Information

TL;DR

This paper investigates the design of symmetric strategies in cooperative multi-agent systems with decentralized information, highlighting the complexities and proposing a modified common information approach for optimization.

Contribution

It introduces a novel framework for symmetric strategies in multi-agent teams, including a modified common information approach and specialized models for private information reduction.

Findings

Randomized symmetric strategies can outperform deterministic ones.

Some existing private information reduction methods are ineffective under symmetry constraints.

A new dynamic programming approach accommodates symmetric strategies in decentralized teams.

Abstract

We consider a cooperative multi-agent system consisting of a team of agents with decentralized information. Our focus is on the design of symmetric (i.e. identical) strategies for the agents in order to optimize a finite horizon team objective. We start with a general information structure and then consider some special cases. The constraint of using symmetric strategies introduces new features and complications in the team problem. For example, we show in a simple example that randomized symmetric strategies may outperform deterministic symmetric strategies. We also discuss why some of the known approaches for reducing agents' private information in teams may not work under the constraint of symmetric strategies. We then adopt the common information approach for our problem and modify it to accommodate the use of symmetric strategies. This results in a common information based dynamic program where each step involves minimization over a single function from the space of an agent's private information to the space of probability distributions over actions. We present specialized models where private information can be reduced using simple dynamic program based arguments.