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 iA_i for each unit, where A_i={10,15,20}.Each firm has associated cost c_i 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 p_i< p_j (i, jN, i j), then the firmisells q_i=Q units and the other firm sells q_j= 0; and if p_i=p_j, then q_i=q_j=Q/2. Firm's profit equals to u(p_i, p_i) = (p_ic_i)q_i(p_i;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).Representthegamebyapayoffmatrixandfindallthepure-strategyNash 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).Representthe game by a payoffmatrixand find all the purestrategy Nash Equilibria in it.