Consider the following variant of the standard Hotelling spacial location model. The set of the product characteristics is [0,1]. There are a finite number of firms whose production costs are all zero. Each firm can produce only one type of product, and thus chooses exactly one characteristic. There is a continuum of consumers whose characteristics (tastes) are uniformly distributed in the product characteristic space. Each consumer buys exactly one unit of the product, and buys from a firm whose product characteristic is closer to his or her own characteristic (and buys with equal probability if s/ he is in an equal distance from both products). The price is fixed exogenously, say at p>0, and the firm's payoff is equal to its profit. 1. Now, assume that there are 3 firms, namely firms 1,2 , and 3 . They choose product characteristics in [0,1] simultaneously. As in the previous case, there the valis ase diridad repuatly by these firmes t tas, then peowe it. (b) (6. poiate) Now, ascume that the firus" paycat lis rtangred and earh lagkst share of cansumers, abil there ace it tinas that seil the largest share thin pagud toe the fiers in arse if is is not one of the thres that well the lasmet share of centamires |lastriot of intergerting thin gome reveives the tarpst vote shate is the witever). In tha mulified gume, (i.e., the veter whine maint prefinted peidey is it the mentias of the vaiters) a f (0,1/2) (and foe rach realinations, the ristrilection of the wotern bas fisll supposet o4 [9,1]]. state what the limit of the Nash epelileinas is as the paraeneter a Fiven finm Consider the following variant of the standard Hotelling spacial location model. The set of the product characteristics is [0,1]. There are a finite number of firms whose production costs are all zero. Each firm can produce only one type of product, and thus chooses exactly one characteristic. There is a continuum of consumers whose characteristics (tastes) are uniformly distributed in the product characteristic space. Each consumer buys exactly one unit of the product, and buys from a firm whose product characteristic is closer to his or her own characteristic (and buys with equal probability if s/ he is in an equal distance from both products). The price is fixed exogenously, say at p>0, and the firm's payoff is equal to its profit. 1. Now, assume that there are 3 firms, namely firms 1,2 , and 3 . They choose product characteristics in [0,1] simultaneously. As in the previous case, there the valis ase diridad repuatly by these firmes t tas, then peowe it. (b) (6. poiate) Now, ascume that the firus" paycat lis rtangred and earh lagkst share of cansumers, abil there ace it tinas that seil the largest share thin pagud toe the fiers in arse if is is not one of the thres that well the lasmet share of centamires |lastriot of intergerting thin gome reveives the tarpst vote shate is the witever). In tha mulified gume, (i.e., the veter whine maint prefinted peidey is it the mentias of the vaiters) a f (0,1/2) (and foe rach realinations, the ristrilection of the wotern bas fisll supposet o4 [9,1]]. state what the limit of the Nash epelileinas is as the paraeneter a Fiven finm
