In recent work by Bramoulle and Kranton, a model for the provision of public goods on a network was presented and relations between equilibria of such a game and properties of the network were established. This model was further extended to include games with imperfect substitutability in Bramoulle et al. The vast multiplicity of equilibria in such games along with the drastic changes in equilibria with small changes in network structure, makes it challenging for a system planner to estimate the maximum social welfare of such a game or to devise interventions that enhance this welfare. Our main results address this challenge by providing close approximations to the maximum social welfare and the maximum aggregate play in terms of only network characteristics such as the maximum degree and independence number. For the special case when the underlying network is a tree, we derive formulae which use only the number of nodes and their degrees. These results allow a system planner to assess aggregate outcomes and design interventions for the game, directly from the underlying graph structure, without enumerating all equilibria of the game, thereby significantly simplifying the planner's problem. A part of our results can be viewed as a logical extension of [7] where the maximum weighted aggregate effort of the model in [2] was characterized as the weighted independence number of the graph.

中文翻译：

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网络战略互动中的综合游戏和福利

在 Bramoulle 和 Kranton 最近的工作中，提出了一个在网络上提供公共物品的模型，并建立了这种博弈的均衡与网络属性之间的关系。该模型进一步扩展到包括 Bramoulle 等人中具有不完全替代性的游戏。此类博弈中的大量均衡以及均衡的剧烈变化和网络结构的微小变化，使得系统规划者难以估计此类博弈的最大社会福利或设计增强这种福利的干预措施。我们的主要结果通过仅在最大程度和独立数等网络特征方面提供对最大社会福利和最大总体发挥的近似值来解决这一挑战。对于底层网络是树的特殊情况，我们推导出仅使用节点数及其度数的公式。这些结果允许系统规划者直接从底层图结构评估游戏的总体结果和设计干预，而无需枚举游戏的所有均衡，从而显着简化规划者的问题。我们的部分结果可以看作是 [7] 的逻辑扩展，其中 [2] 中模型的最大加权聚合努力被表征为图的加权独立数。无需枚举博弈的所有均衡点，从而显着简化了规划者的问题。我们的部分结果可以看作是 [7] 的逻辑扩展，其中 [2] 中模型的最大加权聚合努力被表征为图的加权独立数。无需枚举博弈的所有均衡点，从而显着简化了规划者的问题。我们的部分结果可以看作是 [7] 的逻辑扩展，其中 [2] 中模型的最大加权聚合努力被表征为图的加权独立数。