question archive Two firms selling the external keyboards compete in price of their product
Two firms selling the external keyboards compete in price of their product
Subject:EconomicsPrice: Bought3
Two firms selling the external keyboards compete in price of their product. Set set of players is N={1,2}. The firms are choosing price simultaneously. Firm i∈ {1,2} chooses price i∈Ai for each unit, where Ai={10,15,20}. Each firm has associated cost ci associated with selling each unit. There is Q= 1000 of potential customerseach of who wants to buy exactly one external keyboard. The firm that chooses the lower price wins the market, in other terms if pi< pj (i, j∈N, i ≠j), then the firmisells qi=Q units and the other firm sells qj= 0; and if pi=pj, then qi=qj=Q/2. Firm's profit equals to u(pi, p−i) = (pi−ci)qi(pi;p−i). (Note that since there are only two players in this game,p−i represents the price of the other player j ≠i). Assume that each firm is a profit maximizer (the utility each firm maximizes is equal to its profit).
(a) Suppose c1=c2= 10. Represent the game by a payoff matrix and find all the pure-strategy Nash Equilibria in it.
(b) Suppose c1= 5 and c2= 15 (firm 1 is able to produce more efficiently).Represent the game by a payoff matrix and find all the pure-strategy Nash Equilibria in it.
(c) Suppose that c1=c2= 10 as in (a), but the consumers get indeci-sive whenever p1=p2, and they don't buy from either of the firms as a result (q1=q2= 0). Represent the game by a payoff matrix and find all the purestrategy Nash Equilibria in it.
