ECOS 2201 Economics of Strategy and Competition Semester 2, 2022 Problem Set 3
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ECOS 2201 Economics of Strategy and Competition
Semester 2, 2022
Problem Set 3
1. Consider the following version of a trust game with two players, a firm and a worker. They are both risk neutral. The worker moves first. He can ACQUIRE skills that are specific to the firm that he works with (e.g develop a relationship with a customer) at a cost C > 0 or choose to NOT ACQUIRE skills. These are skills that are only valuable to the firm and not to outside employers. The firm after observing a worker’s skill choice must decide on whether to PAY the worker, B > C (B is assumed to be a parameter here) or NOT PAY the worker. If skills are acquired the firm gets an output of y, otherwise the firm gets an output of 0.
(a) Draw the game tree for this version of the trust game.
(b) Suppose this game is played only once. What is the Nash Equi-
librium?
(c) Now suppose the stage game above is played repeatedly for an infinite number of periods. Assume that the player’s payoffs in this repeated game are the discounted sum of payoffs in each period and denote the interest rate by T . Using grim trigger strategies, find conditions under which the cooperative outcome, where the worker acquires skills and the firm pays the worker if and only if skills are acquired, is a Nash Equilibrium of the repeated game.
2. Consider an infinitely repeated setting with a worker and a firm. In each period, the worker can exert an effort level a anywhere between 0 and 1, which is unobservable to the firm and his effort cost is given by C(a) = a2 . If the worker exerts an effort level of a in a period then with probability a, output is yH = 1 in that period and with probability 1 − a output is yL = 0 in that period. The firm can offer a take it or leave it wage offer to the worker with a contractible salary s paid to the worker if the worker agrees to work for the firm for the period and b is a non-contractible bonus which the firm promises to pay to the worker when yH is realized. Assume that the firm maximizes its discounted sum of expected profits and the worker maximizes the discounted sum of his expected utility (i.e expected wage minus his cost of effort), and denote the interest rate by r . The workers outside wage is wA = 0.1.
(a) Derive the self enforcing constraint that ensures that the firm pays
the bonus when y = yH .
(b) Draw a graph that clearly depicts the self enforcing constraint.
Provide as much information as you can in this picture (e.g inter- cepts, the value of the function at its peak etc).
2022-09-05