标题： 网络约束市场中的均衡与做市商 显示英文标题

标题： Equilibria in Network Constrained Markets with Market Maker

摘要： 我们研究一个由$n$个生产者组成的联网经济系统，这些生产者向多个地理位置分离的市场供应一种单一的同质商品，并有一个中央机构，称为市场中介。 生产者通过选择他们可以进入的每个市场的供应数量来进行古诺竞争，以最大化他们的利润。 每个市场都有其反需求函数，该函数将所考虑商品的单位价格作为总可用数量的函数。 市场通过一个输电网络相互连接，通过该网络，所考虑商品的数量可以在有限容量约束下流动。 这些流量由市场中介确定，其目标是最大化指定的社会福利函数。 我们将这种竞争建模为一个具有$n+1$个参与者的策略博弈：生产者和市场博弈。 对于这个博弈，我们在标准凹性假设下首先建立了纳什均衡的存在性。 然后，我们确定了博弈为势博弈的充分条件，并且纳什均衡基本上是唯一的。 接下来，我们提出一个一般性结果，将市场中介的最佳行动与对网络施加的容量约束联系起来。 对于常用的瓦尔拉社会福利，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的联系。 这一现象在现实世界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。 显示英文摘要

摘要： 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 \`a 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. Such flows are determined by the market maker, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the market game. For this game, we first establish the existence of Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the market maker 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.