At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,10]. The manager of these 20 employees announces that she will contribute d dollars for every dollar that an employee contributes. The payoff to employee i who makes contribution of x; dollars is bi(1+d)xi-xi, where b; > 0. Assume that d = 2, b;= 0.25 for i=1,2,..., 10, and

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.7P
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At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many
dollars to contribute from the interval [0,10]. The manager of these 20 employees announces that she will contribute d dollars
for every dollar that an employee contributes.
The payoff to employee i who makes contribution of x; dollars is
b;(1+d)x; – ai, where b; > 0.
Assume that d = 2, b; = 0.25 for i = 1,2,..., 10, and
bị
= 0.5 for i = 11, 12, ..., 20.
What is the total contribution level in the Nash equilibrium by the 20 employees (that is, excluding the contribution by the
manager).
Numerical answer
Transcribed Image Text:At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,10]. The manager of these 20 employees announces that she will contribute d dollars for every dollar that an employee contributes. The payoff to employee i who makes contribution of x; dollars is b;(1+d)x; – ai, where b; > 0. Assume that d = 2, b; = 0.25 for i = 1,2,..., 10, and bị = 0.5 for i = 11, 12, ..., 20. What is the total contribution level in the Nash equilibrium by the 20 employees (that is, excluding the contribution by the manager). Numerical answer
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