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 $20,000 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) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium. b) 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 $30,000. c) In the only Nash equilibrium for this game, both partners earn $30,000. d) In the only Nash equilibrium for this game, both partners earn $100,000. e) In the only Nash equilibrium for this game, one partner earns $60,000 and the other earns $40,000.
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 $20,000 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) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.
b) 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 $30,000.
c) In the only Nash equilibrium for this game, both partners earn $30,000.
d) In the only Nash equilibrium for this game, both partners earn $100,000.
e) In the only Nash equilibrium for this game, one partner earns $60,000 and the other earns $40,000.
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