A Stackelberg duopoly model in which two firms compete to maximize their market share is considered. The firms offer a service/product to customers that are spread over several geographical regions (e.g., countries, provinces, or states). Each region has its own characteristics (spreading and recovery rates) of each service propagation. We consider that the spreading rate can be controlled by each firm and is subject to some investment that the firm does in each region. One of the main objectives of this work is to characterize the advertising budget allocation strategy for each firm across regions to maximize its market share when competing. To achieve this goal we propose a Stackelberg game model that is relatively simple while capturing the main effects of the competition for market share. {By characterizing the strong/weak Stackelberg equilibria of the game, we provide the associated budget allocation strategy.} In this setting, it is established under which conditions the solution of the game is the so-called ``winner takes all". Numerical results expand upon our theoretical findings and we provide the equilibrium characterization for an example.

翻译：本文考虑一个Stackelberg双寡头模型，其中两家企业竞相最大化其市场份额。这些企业向分布在不同地理区域（如国家、省份或州）的客户提供服务/产品。每个区域均具有各自的服务传播特性（传播率和恢复率）。我们假设传播率可由每家企业控制，且取决于企业在各区域的投资水平。本研究的主要目标之一是，在竞争环境下刻画企业跨区域广告预算分配策略以最大化市场份额。为实现该目标，我们提出一个相对简洁却能够捕捉市场份额竞争主要效应的Stackelberg博弈模型。通过刻画博弈的强/弱Stackelberg均衡，我们给出了相应的预算分配策略。在该设定下，我们确定了博弈解呈现所谓“赢家通吃”的条件。数值实验拓展了理论发现，并通过一个实例给出了均衡刻画。