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.

翻译：我们证明了网络博弈中一个普遍存在的特征——双边策略互动——等价于参与者的效用函数在对手之间具有可加可分性。我们区分了双边策略互动的两种形式化概念。对手独立性意味着参与者i对于对手j行动的偏好不依赖于其他对手的行为。策略独立性意味着对手j的选择如何影响i在任意两种行动之间的偏好不依赖于其他对手的行为。若i的偏好同时满足这两个条件，则我们可以使用可加可分的效用函数来表示她对策略组合的偏好。若i的偏好仅满足策略独立性，我们仍可使用可加可分的效用函数来表示她仅针对自身行动的偏好。基于对手行动线性聚合的常见效用函数满足策略独立性，因此在策略上等价于可加可分的效用函数——事实上，我们可以假设效用函数在对手行动上是线性的。