Potential Games Design Using Local Information

TL;DR

This paper develops a method to design potential games using only local information, enabling system-level objectives to be achieved in multiagent systems with limited data sharing.

Contribution

It introduces a systematic approach to verify and compute local utility functions that ensure potential game properties with minimal information exchange.

Findings

The existence of local utility functions can be checked via linear equations.

An algorithm is proposed to compute local utility functions when solutions exist.

Application to multiagent consensus demonstrates the method's effectiveness.

Abstract

Consider a multiplayer game, and assume a system level objective function, which the system wants to optimize, is given. This paper aims at accomplishing this goal via potential game theory when players can only get part of other players' information. The technique is designing a set of local information based utility functions, which guarantee that the designed game is potential, with the system level objective function its potential function. First, the existence of local information based utility functions can be verified by checking whether the corresponding linear equations have a solution. Then an algorithm is proposed to calculate the local information based utility functions when the utility design equations have solutions. Finally, consensus problem of multiagent system is considered to demonstrate the effectiveness of the proposed design procedure.