We consider a commerce platform that consists of two queues: one for buyers of an item and the other for sellers of the item. The platform is operated under the first-join-first-trade discipline. Upon a trade, the buyer and the seller gain respective profits but incur the cost of waiting in the platform. To maximize their expected payoffs from trading, both buyers and sellers can choose their arrival times. We characterize the Nash equilibrium in terms of a system of integro-differential equations for arrival time distributions. We show that a unique Nash equilibrium exists by proving that the system of integro-differential equations has a unique solution. Additionally, we compute the price of anarchy and investigate other disciplines that can improve it. Specifically, we show that charging platform usage fees improves the price of anarchy.

中文翻译：

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商务平台的战略入场时间

我们认为一个商务平台由两个队列组成：一个用于商品的买家，另一个用于商品的卖家。该平台按照先加入先交易规则运营。在交易中，买方和卖方获得各自的利润，但会产生在平台中等待的成本。为了最大限度地提高他们从交易中获得的预期回报，买家和卖家都可以选择他们的到达时间。我们根据到达时间分布的积分微分方程组来表征纳什均衡。我们通过证明积分微分方程组具有唯一的解来证明存在唯一的 Nash 均衡。此外，我们计算无政府状态的代价并研究其他可以改善它的学科。具体来说，我们表明收取平台使用费可以提高无政府状态的价格。