Consider the employee-employer relationship - an employee would like to be paid but also gets some benefit by shirking his duties. An employer would like the employee to work diligently but monitoring the employee is costly. This dynamic can be modeled using a game. The payoffs of the "monitoring game" are given below:
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Business
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Monitor
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Don't Monitor
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Shirk
Employee
Work
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0, -20
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150, -100
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100, 80
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100, 100
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For the employer, this assumes that the worker receives 100 in wages, produces 200 worth of goods if the employee works and monitoring costs 20. From the employee's point of view, the net benefit to the employee from working and getting paid is 100. If the worker can shirk and get paid the worker is better off, however the employee is fired if the worker shirks and the employer monitors and thus is worse off.
- Show that there are no pure strategy Nash equilibria in this game.
- What is the mixed strategy Nash equilibria? In other words, what is the probability that the employer will monitor? What is the probability that the employee will shirk? See the lecture for details on how to calculate the probabilities.
- Briefly interpret the Nash equilibria in words.