1. The technology of interaction for a contractual relationship is given by the matrix below. 2 H L 1 H 5,5 0,8 L 7,0 1,1 Suppose the players write an incomplete contract stating that they agree to play the jointly-efficient outcome (that which maximizes the joint payoff as found in last week's homework). Assume that the court can verify exactly the outcome of produc-

2. Consider an infinitely repeated game in which, in each period, two firms with zero costs choose quantities and prices are given by: p1 = 1 - q1 - q2/2, p2 = 1 - q2 - q1/2. Firms have a common discount factor of 8 = 1/2. a) Explain what a trigger strategy is and determine whether the firms can attain the joint profit maximising outcome in a subgame perfect equilibrium using trigger strategies. b) Explain what a stick and carrot strategy is and discuss whether it is possible to attain the joint-profit maximising outcome in a subgame perfect equilibrium using stick and carrot strategies.

Consider the following game. Player 1 has three actions: A, B, C. Player 2 has three actions: a, b.c. Payoffs are as follows: a b A 5,3 8,5 1,2 2,6 6,7 4,5 C 4,4 0,2 9,3 Which of the following aciton profile survives the iterated elimination of strongly dominated actions? A. (A,a) O B. (B, c) O C. (A, b)

3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W x y Z 2,1 0,2 2,1 a 3,3 b 1,1 1,2 1,0 1,4 c 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 Find all the Nash equilibria in the game in pure strategies.

Consider the infinite repeated two-player game where at each stage the play- ers play the non-zero-sum game given by A В A (5, 5) (0,7) В (7, 0) | (2, 2) (a) Consider the following strategies: SA: always play A. SB: always play B. • St: play A on the first stage, thereafter copy what the other player did in the preceding stage. Suppose that the total payoff involves a discount factor 8, and that both players are restricted to the pure strategies SA, SB, and sT. Determine the set of d for which (ST, ST) is a Nash equilibrium. (b) Use the one stage deviation principle to determine whether the pair (ST, ST) is a subgame perfect Nash equilibrium for some range of val- ues of 8.

A 201.

The hand written is not allowed.

i need it in words not handwritten