located in the same place) no Nash equilibrium price pair (in pure strategies) exists for the second stage subgame (because there is an incentive to undercut the rival firm's price and gain the entire market). For example, when firms are equidistant from the centre of the street, no equilibrium price pair exists for locations 1/4 or closer than 1/4 of the length of the street from the centre. The non-existence of a Cournot equilibrium precludes the ending of the game, and so it is not repeated. Thus, although both firms at the halfway point itself is an equilibrium, there is no tendency for firms to agglomerate here. If only Firm x can relocate without costs and Firm y is fixed, Firm x will move to the side of Firm y where the consumer pool is maximized. Consequently, the profits for Firm X significantly increase, while the profits for Firm Y significantly decrease. Salop’s Circle Model One of the most famous variations of Hotelling’s location model is Salop’s circle model. Similar to the previous spatial representations, the circle model examines consumer preference with regards to geographic location. However, Salop introduces two significant factors: 1) firms are located around a circle with no end-points, and 2) it allows the consumer to choose a second, heterogeneous good. An example of a second good Assumptions Assume that the consumers are equidistant from one another around the circle. The model will occur for one time period, in which only one product is purchased. The consumer will have a choice of purchasing variations of Product A (a differentiated product) or Product B (an outside good; undifferentiated product). There are two firms also located equidistant around the circle. Each firm offers a variation of Product A, and an outside firm offers a good, Product B. Analysis In this example, the consumer wants to purchase their ideal variation of Product A. They are willing to purchase the product, given that it is within the constraint of their utility, transportation/distance costs, and price. The utility for a particular product at distance is represented in the following equation: Where is the utility from a superior brand, denotes the rate at which an inferior brand lowers the utility from the superior brand, is the location of the superior brand, and is the location of the consumer. The distance between the brand and the consumer is thereby given in . The consumer’s