We study a networked economic system composed of $n$ producers supplying a single homogeneous good to a number of geographically separated markets and of a centralized authority, called the market maker. Producers compete à la Cournot, by choosing the quantities of good to supply to each market they have access to in order to maximize their profit. Every market is characterized by its inverse demand functions returning the unit price of the considered good as a function of the total available quantity. Markets are interconnected by a dispatch network through which quantities of the considered good can flow within finite capacity constraints and possibly satisfying additional linear physical constraints. Such flows are determined by the action of a system operator, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the system operator. For this game, we first establish the existence of pure-strategy Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be exact potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the system operator with the capacity constraints imposed on the network. For the commonly used Walrasian welfare, our finding proves a connection between capacity bottlenecks in the market network and the emergence of price differences between markets separated by saturated lines. This phenomenon is frequently observed in real-world scenarios, for instance in power networks. Finally, we validate the model with data from the Italian day-ahead electricity market.

翻译：我们研究由 $n$ 个生产商、多个地理分离的市场以及一个称为做市商的中央权威机构组成的网络化经济系统。生产商以古诺方式竞争，通过选择向每个可进入市场供应的商品数量来最大化利润。每个市场由其逆需求函数刻画，该函数将考虑商品的总可用数量映射为单位价格。市场通过调度网络互联，商品数量可在有限容量约束下在该网络中流动，并可能满足额外的线性物理约束。这些流量由系统运营商的行动决定，其目标是最大化指定的福利函数。我们将此竞争建模为包含 $n+1$ 个参与者的策略博弈：生产商和系统运营商。针对此博弈，我们首先在标准凹性假设下建立了纯策略纳什均衡的存在性。然后，我们确定了博弈成为精确势博弈且具有本质唯一纳什均衡的充分条件。接着，我们提出一个通用结果，将系统运营商的最优行动与网络上的容量约束联系起来。对于常用的瓦尔拉斯福利，我们的发现证明了市场网络中的容量瓶颈与由饱和线路分隔的市场之间价格差异的出现之间存在联系。这种现象在现实场景中经常被观察到，例如在电力网络中。最后，我们使用意大利日前电力市场的数据验证了该模型。