Bayesian Quadratic Network Game Filters

TL;DR

This paper introduces the Quadratic Network Game (QNG) filter, enabling agents in a network to iteratively update beliefs, choose optimal actions, and learn the network's state in quadratic utility games with externalities.

Contribution

It presents the novel QNG filter that allows decentralized belief updating and action selection in quadratic network games with externalities.

Findings

QNG filter effectively estimates the network's state.

Demonstrated on Cournot competition and coordination games.

Enables autonomous team navigation with improved decision-making.

Abstract

A repeated network game where agents have quadratic utilities that depend on information externalities -- an unknown underlying state -- as well as payoff externalities -- the actions of all other agents in the network -- is considered. Agents play Bayesian Nash Equilibrium strategies with respect to their beliefs on the state of the world and the actions of all other nodes in the network. These beliefs are refined over subsequent stages based on the observed actions of neighboring peers. This paper introduces the Quadratic Network Game (QNG) filter that agents can run locally to update their beliefs, select corresponding optimal actions, and eventually learn a sufficient statistic of the network's state. The QNG filter is demonstrated on a Cournot market competition game and a coordination game to implement navigation of an autonomous team.