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The utility functions of two individuals are U; = 206, +) - 15e, and U2 = 10(e+ ey) - 15€, where e, is the effort contributed by individual 1 and e, is the effort contributed by individual 2

Economics Nov 11, 2020

The utility functions of two individuals are U; = 206, +) - 15e, and U2 = 10(e+ ey) - 15€, where e, is the effort contributed by individual 1 and e, is the effort contributed by individual 2. Each individual i can set e, equal to any number between zero and one inclusive Derive the best responses of individuals. Justify your answer What is the Nash equilibrium of this game? Explain your answer and give an intuitive explanation of the derived equilibrium. [33%)
Derive the best responses of individuals. Justify your answer What is the Nash equilibrium of this game? Explain your answer and give an intuitive explanation of the derived equilibrium. Ant

Expert Solution

Since the marginal return on effort of Agent 1 is constant ,positive and independent of effort of agent 2, Agent 1 best response is to put max effort i.e. 1

Since marginal return on effort of Agent 2 is negative, constant and independent of efforts of agent 1, Agent 2 best response is to put min effort i.e. 0

Hence Nash equilibrium is (1,0).

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