The basic framework is Hotelling’s model of product choice with quadratic transportation cost. Duopolists choose locations in the initial period and compete in prices in subsequent infinite periods. The firms share profits on the profit possibility frontier. Friedman and Thisse (Rand J Econ 24:631–645, 1993) provides a set of sufficient conditions for a unique equilibrium and minimal product differentiation in this setting. This paper reexamines those conditions. In the presence of some mild continuity requirements, there is exactly one profit sharing rule which satisfies those conditions. Furthermore, given any discount factor(s), the corresponding profits cannot be the outcome of a subgame perfect Nash equilibrium at every pair of locations. This brings out an inconsistency in the conditions. A slight weakening of the conditions, to allow for a wider class of profit sharing rules, can result in multiple equilibria and minimal product differentiation need not obtain. Two examples demonstrate this. Thus, neither those conditions nor their weaker variants can be used to characterize a unique equilibrium.

基本框架是Hotelling的产品选择模型，其运输成本为二次方。Duopolists在初始阶段选择地点，并在随后的无限时期内竞争价格。这些公司在利润可能性边界上分享利润。Friedman and Thisse（Rand J Econ 24：631–645，1993）为在这种情况下实现独特的平衡和最小的产品差异提供了一组充分的条件。本文重新审查了这些条件。在存在一些适度的连续性要求的情况下，恰好有一条满足这些条件的利润分配规则。此外，在给定任何折扣因子的情况下，相应的利润不能是每对位置的子博弈完美纳什均衡的结果。这带来了条件上的不一致。条件略有减弱，允许更广泛的利润分享规则，可能会导致多重均衡，并且不需要获得最小的产品差异。有两个例子证明了这一点。因此，这些条件或其较弱的变体都不能用来表征唯一的平衡。