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Problem 3 Consider a firm that employs a worker on a project. If the project succeeds, it generates a revenue of a > 0 for the firm. If it fails, the revenue is zero. The worker can choose an effort level e = 0 or e = 1. If he chooses e = 0, the project succeeds with probability po; if he chooses e = 1, the project succeeds with probability p₁> po. The firm does not observe the actual effort, only the whether the project succeeds or not. Hence, it sets a wage schedule such that it pays a wage of ws in case the project succeeds, and of wp in case of failure. Both wages cannot be negative. The worker's utility is given by w- ce, with a > c>0. The firm maximizes expected profits. Both players are risk neutral. The game proceeds as follows: Step 1: The firm sets the wage schedule Step 2: The worker decides about his effort. Step 3: Nature decides whether the project fails or not (with probabilities depending on the effort chosen in step 2), and the payoffs are realized. 1. Write down the game tree 2. Find the players' payoff functions. 3. Find the subgame perfect equilibrium.

Problem 3 Consider a firm that employs a worker on a project. If the project succeeds, it generates a revenue of a > 0 for the firm. If it fails, the revenue is zero. The worker can choose an effort level e = 0 or e = 1. If he chooses e = 0, the project succeeds with probability po; if he chooses e = 1, the project succeeds with probability p₁> po. The firm does not observe the actual effort, only the whether the project succeeds or not. Hence, it sets a wage schedule such that it pays a wage of ws in case the project succeeds, and of wp in case of failure. Both wages cannot be negative. The worker's utility is given by w- ce, with a > c>0. The firm maximizes expected profits. Both players are risk neutral. The game proceeds as follows: Step 1: The firm sets the wage schedule Step 2: The worker decides about his effort. Step 3: Nature decides whether the project fails or not (with probabilities depending on the effort chosen in step 2), and the payoffs are realized. 1. Write down the game tree 2. Find the players' payoff functions. 3. Find the subgame perfect equilibrium.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 3 Consider a firm that employs a worker on a project. If the project succeeds, it generates a revenue of a > 0 for the firm. If it fails, the revenue is zero. The worker can choose an efort level e = 0 or e = 1. If he chooses e = 0, the project succeeds with probability po; if he chooses e = 1, the project succeeds with probability pi > po. The firm does not observe the actual effort, only the whether the project succeeds or not. Hence, it sets a wage schedule such that it pays a wage of ws in case the project succeeds, and of wp in case of failure. Both wages cannot be negative. The worker's utility is given by w – ce, with a > c > 0. The firm maximizes expected profits. Both players are risk neutral. The game proceeds as follows: Step 1: The firm sets the wage schedule Step 2: The worker decides about his effort. Step 3: Nature decides whether the project fails or not (with probabilities depending on the effort chosen in step 2), and the payoffs are realized. 1. Write down the game tree 2. Find the players' payoff functions. 3. Find the subgame perfect equilibrium.
Transcribed Image Text:Problem 3 Consider a firm that employs a worker on a project. If the project succeeds, it generates a revenue of a > 0 for the firm. If it fails, the revenue is zero. The worker can choose an efort level e = 0 or e = 1. If he chooses e = 0, the project succeeds with probability po; if he chooses e = 1, the project succeeds with probability pi > po. The firm does not observe the actual effort, only the whether the project succeeds or not. Hence, it sets a wage schedule such that it pays a wage of ws in case the project succeeds, and of wp in case of failure. Both wages cannot be negative. The worker's utility is given by w – ce, with a > c > 0. The firm maximizes expected profits. Both players are risk neutral. The game proceeds as follows: Step 1: The firm sets the wage schedule Step 2: The worker decides about his effort. Step 3: Nature decides whether the project fails or not (with probabilities depending on the effort chosen in step 2), and the payoffs are realized. 1. Write down the game tree 2. Find the players' payoff functions. 3. Find the subgame perfect equilibrium.
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