A Theory of Network Games Part 1: Utility Representations
For game theorists and economists, this work offers principled generalizations and clarifies the theoretical underpinnings of commonly used utility models in network games.
The paper provides axiomatic foundations for utilities in network games, showing that bilateral strategic interactions imply additively separable utilities, and identifies conditions that pin down the classic linear-quadratic utility.
We provide interpretable axiomatic foundations for utilities used in network games and identify several principled generalizations. First, we demonstrate that a ubiquitous feature of network games, bilateral strategic interactions, is equivalent to having player utilities that are additively separable across opponents. Common utilities based on a linear aggregate of opponent actions are strategically equivalent to additively separable utilities. Moreover, assuming real-valued actions, we show that a constant rate of substitution between opponents implies a utility that is linear in opponent actions. Finally, we identify precise conditions--linear best replies and midpoint indifference--that pin down the classic linear-quadratic utility.