Expansibility Research And Game Analysis Of Hotelling Model

In real life, price competition and production competition are the main forms of firms competition in market. In short run, price changing can often be easily observed by people. Bertrand studied two oligopoly firms competing on price in the market under the assumption that the cost structure and product characteristics are rigid. We found that oligopoly firms price according to marginal cost as the same with fully competitive firms. That is, firms'number does not matter for their pricing. This is the famous Bertrand paradox. But a crucial assumption of Bertrand paradox is all the firms producing the same type of products that we call it product with indifference and with complete-subsititution. Therefore, price is the only variable which consumers are interested in, and no one firm can raise the price above the marginal cost without losing its market share. But in reality, these assumptions are often unsatisfiable.Product differentiation is very important on studying market structure. Hotelling (1929) first studied the price competition with product-difference. In his paper, the product-difference is interpreted as different firm-location. In his model, under the condition of existence of the travel costs, Hotelling proved the equilibrium price exceeds the marginal cost and all two firms can gain positive profits, and solved the Bertrand paradox. Since then, there are many literatures in studying the Hotelling model.Based on previous Hotelling model literatues, this paper mainly expands the Hotelling model with follows: I select two firms and discuss their price competiting and locating under different conditions. Using game theory, this paper mainly discuss the two kinds situations that marginal production cost and transportation cost are all different. Then on the latter situation, this paper has discussed three situations: the two firms simultaneously choose a single price, the two firms choose discriminatory pricing, and one manufacturer choose uniform pricing and another choose discriminatory pricing. Then I discussed the situation of the two firms pricing-location when transport costs can be transfered: one of the two firms provide free shopping cart, or two firms all don't provide free shopping cart, or two firms all provide free shopping cart. If we expand the Hotelling model with network externalities, then there are three different situation to analysis respectively: having the same externality coefficient and having different externality coefficient. and then analyze the network externalities effects on the manufacturer's pricing-locating by contrasting with the situation of no externalities. The finally part is the summarizes this paper and advances several problems to be futher developped.