Game Networks

TL;DR

Game networks (G nets) offer a structured, compact, and computationally efficient framework for multi-agent decision problems, enabling easier strategic inference and equilibrium computation.

Contribution

Introduction of G nets as a novel, structured representation for multi-agent decision problems that enhances computational efficiency and equilibrium analysis.

Findings

G nets are more structured and compact than traditional game representations.

G nets enable simplified strategic inference through probability and utility independencies.

New convergence methods for identifying strategic equilibria using G nets.

Abstract

We introduce Game networks (G nets), a novel representation for multi-agent decision problems. Compared to other game-theoretic representations, such as strategic or extensive forms, G nets are more structured and more compact; more fundamentally, G nets constitute a computationally advantageous framework for strategic inference, as both probability and utility independencies are captured in the structure of the network and can be exploited in order to simplify the inference process. An important aspect of multi-agent reasoning is the identification of some or all of the strategic equilibria in a game; we present original convergence methods for strategic equilibrium which can take advantage of strategic separabilities in the G net structure in order to simplify the computations. Specifically, we describe a method which identifies a unique equilibrium as a function of the game payoffs, and one which identifies all equilibria.