Online-Offline Competition with Heterogeneous Consumers: An Example for No Existence of Pure Strategy Nash Equilibrium

Weixing Ford, Haipeng Han, Jie Zheng
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Abstract

Existing literature on competition between online and offline firms has focused on market conditions that guarantee the existence of a pure strategy Nash equilibrium. In this note, by constructing a concrete example, we provide a first attempt to show that the equilibrium existence result does not necessarily hold when consumers’ preferences are heterogeneous. Specifically, we consider the competition between one online firm and several offline firms in a market organized as a Salop model, where consumers’ preferences have a binary distribution. We identify a boundary scenario where the type distribution is binary with one type of consumer loyal to online shopping and the other type loyal to offline shopping. We show that there is no pure strategy Nash equilibrium for this boundary scenario, which indicates that the market may not be stable under such conditions. Our study contributes to a better understanding of the equilibrium existence conditions for the online versus offline retail competition.
异质性消费者的线上线下竞争:纯策略纳什均衡不存在的一个例子
现有的关于线上和线下公司之间竞争的文献集中在保证纯战略纳什均衡存在的市场条件上。在本文中,通过构建一个具体的例子,我们首次尝试证明,当消费者的偏好是异质的时,均衡存在的结果并不一定成立。具体地说,我们考虑一个市场中一个线上公司和几个线下公司之间的竞争,在这个市场中,消费者的偏好是二元分布的。我们确定了一个边界场景,其中类型分布是二元的,一种类型的消费者忠诚于在线购物,另一种类型的消费者忠诚于离线购物。我们证明了在这种边界情况下不存在纯策略纳什均衡,这表明在这种情况下市场可能不稳定。我们的研究有助于更好地理解线上与线下零售竞争的均衡存在条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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