Asked by Jaida McNair on Jun 13, 2024
Verified
Two partners start a business.Each has two possible strategies, spend full time or secretly take a second job and spend only part time on the business.Any profits that the business makes will be split equally between the two partners, regardless of whether they work full time or part time for the business.If a partner takes a second job, he will earn $60,000 from this job plus his share of profits from the business.If he spends full time on the business, his only source of income is his share of profits from this business.If both partners spend full time on the business, total profits will be $200,000.If one partner spends full time on the business and the other takes a second job, the business profits will be $80,000.If both partners take second job, the total business profits are $20,000.
A) In the only Nash equilibrium for this game, both partners earn $70,000.
B) In the only Nash equilibrium for this game, one partner earns $100,000 and the other earns $40,000.
C) In the only Nash equilibrium for this game, both partners earn $100,000.
D) This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $70,000.
E) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.
Second Job
Additional employment taken on by an individual in addition to their primary job, often to supplement income.
Full Time
Employment status where individuals work a minimum number of hours defined by their employer as full-time.
Business Profits
The excess of revenues generated from business activities over the costs incurred in producing those revenues, reflecting the financial success of a business.
- Comprehend the principle of Nash equilibria within the framework of game theory and its practical uses.
- Assess the results of games that incorporate mixed strategies and recognize the prerequisites for their presence.
Verified Answer
GR
Gabby RevellJun 16, 2024
Final Answer :
D
Explanation :
To find the Nash equilibrium, we need to find the strategy for each player where they have no incentive to change their strategy given the strategy of the other player.
Case 1: Both partners spend full time on the business
In this case, neither partner has an incentive to change their strategy since any deviation will result in a lower profit. Therefore, this is a Nash equilibrium.
Case 2: One partner spends full time on the business and the other takes a second job
If one partner spends full time on the business, the other partner has two options: to take a second job or spend full time on the business. If the other partner takes a second job, he earns $60,000 + $40,000 = $100,000. If he spends full time on the business, profits will be split equally between the two partners, so each partner will earn $40,000 + $40,000 = $80,000. Therefore, if one partner spends full time on the business, the other partner has an incentive to take a second job. This is also a Nash Equilibrium.
Case 3: Both partners take a second job
In this case, each partner earns $60,000 + $10,000 = $70,000. Neither partner has an incentive to switch strategies, so this is also a Nash Equilibrium.
Therefore, there are two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $70,000, making choice D the correct answer.
Case 1: Both partners spend full time on the business
In this case, neither partner has an incentive to change their strategy since any deviation will result in a lower profit. Therefore, this is a Nash equilibrium.
Case 2: One partner spends full time on the business and the other takes a second job
If one partner spends full time on the business, the other partner has two options: to take a second job or spend full time on the business. If the other partner takes a second job, he earns $60,000 + $40,000 = $100,000. If he spends full time on the business, profits will be split equally between the two partners, so each partner will earn $40,000 + $40,000 = $80,000. Therefore, if one partner spends full time on the business, the other partner has an incentive to take a second job. This is also a Nash Equilibrium.
Case 3: Both partners take a second job
In this case, each partner earns $60,000 + $10,000 = $70,000. Neither partner has an incentive to switch strategies, so this is also a Nash Equilibrium.
Therefore, there are two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $70,000, making choice D the correct answer.
Learning Objectives
- Comprehend the principle of Nash equilibria within the framework of game theory and its practical uses.
- Assess the results of games that incorporate mixed strategies and recognize the prerequisites for their presence.