game theory

Problem 3: Consider the following three firm version of Bertrand pricing game that we discussed in class. Three firms each simultaneously choose a price p1, P2, p3 2 0. There is one consumer whose demand function is given by: q(p) = 120 - p. Since all three firms produce the same product, the consumer buys goods only from the lowest price firm. If the lowest price is offered by more than one firm, then these firms equally share the quantity demanded. Suppose that all firms have the same marginal cost of production of 10. Part a: What is an example of a Nash equilibrium in this game in which each firm chooses the same price? Part b: Besides the equilibrium that you found in part a, find another Nash equilibrium. Part c: What are all of the Nash equilibria of this game? Part d: Is there a Nash equilibrium that is Pareto efficient in this game? If no Nash equilibria are Pareto efficient, then provide an example of a strategy profile that is Pareto efficient. Part d:/Extra Credit) Consider the 10 firm version of the above game. In this case, what are all of the Nash equilibria