This paper studies a class of network games with linear-quadratic payoffs and externalities exerted through a strictly concave interaction function. This class of game is motivated by the diminishing marginal effects with peer influences. We analyze the optimal pricing strategy for this class of network game. First, we prove the existence of a unique Nash Equilibrium (NE). Second, we study the optimal pricing strategy of a monopolist selling a divisible good to agents. We show that the optimal pricing strategy, found by solving a bilevel optimization problem, is strictly better when the monopolist knows the network structure as opposed to the best strategy agnostic to network structure. Numerical experiments demonstrate that in most cases, the maximum revenue is achieved with an asymmetric network. These results contrast with the previously studied case of linear interaction function, where a network-independent price is proven optimal with symmetric networks. Lastly, we describe an efficient algorithm to find the optimal pricing strategy.

翻译：本文研究一类具有线性-二次收益并通过严格凹交互函数施加外部性的网络博弈。该类博弈的动机源于同伴影响造成的边际效应递减现象。我们分析了这类网络博弈的最优定价策略。首先，我们证明了唯一纳什均衡的存在性。其次，研究垄断者向代理人销售可分商品的最优定价策略。研究表明，相较于无视网络结构的最优策略，垄断者掌握网络结构时通过求解双层优化问题得到的最优定价策略严格更优。数值实验表明，在多数情况下，非对称网络可实现最大收益。这些结果与先前研究的线性交互函数情形形成对比——在线性交互函数情形中，已证明对于对称网络而言，与网络结构无关的定价策略是最优的。最后，我们描述了一种求解最优定价策略的高效算法。