Question

Problems 3,4 and 5

Problem 3. Consider the game below. (a) There are no dominant or dominated strategies. Is there anything you can say about what players will do? Player 2 C T (2,1) (0,2) M (1,1) (1,1)| (1,0) B(0,1) (2,0) (2,2) (0,3) Player (b) Report the best responses Problem 4. Bertrand Competition With Different Costs Suppose two firms facing a demand Dip) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost e and Firm 2 has a marginal cost e. Assume e < e2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p=e and p2= c2 is not a Bertrand equilibrium Problem 5. Cournot Competition Suppose there are two identical firms engaged in quantity competition (Cournot competition). The demand is P =1- Q where Q = +2 Assume that firm's i total cost of production is TC(g) Compute the Cournot equilibrium (i.e., quantities, price, and profits)

Answer 1

Q.3.

a)

Although there are no dominant or dominated strategies in this game, but this game has a unique Nash equilibrium given by

(B,R). Hence in the equilibrium, player 1 will be playing B and player 2 will be playing R both of them receiving payoff of 2 units each.

b)

Let us first write the best response of the player 1 for different actions of player 2. Remember best response is the response which maximizes a player's payoff given the action taken by the other players.

BR1 (L) T BR1 (C) B BR1 (R) B

Similarly writing the best response of player 2, we get:

BR2(T) = R BR2 (M)L, C} BR2(B) R (Both actions give the same payoff)

As we can see from the best responses,

BR1(R) B and BR2(B) = R

and Nash equilibrium is given by the intersection of the best response function.

Hence Nash equilibrium is (B,R) as we obtained in part (a).