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t generates a revenue of a > 0 for the firm. If it fails, the revenue is zero. The worke an choose an effort level e = 0 or e = 1. If he chooses e = 0, the project succeeds witl probability po; if he chooses e = 1, the project succeeds with probability p1 > po. The firn

t generates a revenue of a > 0 for the firm. If it fails, the revenue is zero. The worke an choose an effort level e = 0 or e = 1. If he chooses e = 0, the project succeeds witl probability po; if he chooses e = 1, the project succeeds with probability p1 > po. The firn

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 0, the project succeeds with 1, the project succeeds with probability p1 > p0. The firm does not observe the actual effort, only the whether the project succeeds or not. Hence, it can choose an effort level e = 0 or e = 1. If he chooses e = probability po; if he chooses e = 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 0, the project succeeds with 1, the project succeeds with probability p1 > p0. The firm does not observe the actual effort, only the whether the project succeeds or not. Hence, it can choose an effort level e = 0 or e = 1. If he chooses e = probability po; if he chooses e = 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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