A Theory of Network Games Part 1: Utility Representations

TL;DR

This paper establishes that bilateral strategic interactions in network games can be represented through additively separable utilities, clarifying the conditions under which utilities are independent or strategically independent.

Contribution

It introduces formal notions of opponent independence and strategic independence, showing their implications for utility representations in network games.

Findings

Bilateral interactions are equivalent to additively separable utilities under certain conditions.

Opponent independence implies preferences do not depend on other opponents' actions.

Linear utilities based on opponent actions satisfy strategic independence and are equivalent to additive utilities.

Abstract

We demonstrate that a ubiquitous feature of network games, bilateral strategic interactions, is equivalent to having player utilities that are additively separable across opponents. We distinguish two formal notions of bilateral strategic interactions. Opponent independence means that player i's preferences over opponent j's action do not depend on what other opponents do. Strategic independence means that how opponent j's choice influences i's preference between any two actions does not depend on what other opponents do. If i's preferences jointly satisfy both conditions, then we can represent her preferences over strategy profiles using an additively separable utility. If i's preferences satisfy only strategic independence, then we can still represent her preferences over just her own actions using an additively separable utility. Common utilities based on a linear aggregate of opponent actions satisfy strategic independence and are therefore strategically equivalent to additively separable utilities--in fact, we can assume a utility that is linear in opponent actions.