Two students N = {1,2} are involved in a team project. If both students devote more...

 

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Two students N = {1,2} are involved in a team project. If both students devote more effort to the project, they are both better off. Specifically, an effort level is a nonnegative real number, and student 1's payoff function is e₁ (1 + €2-e₁), where e₁ is student 1's effort level, and e2 is student 2's effort level. The cost of effort is higher for student 2 such that her payoff function is given as e2 (1 + 1 - 2e2). (a) Suppose that both students decide their effort levels simultaneously. Find all pure strategy Nash equilibria. (b) Suppose that student 1 decides her effort level first, and after student 2 observes it, she decides her effort level. Find all subgame perfect Nash equilibria, and their outcomes. Two students N = {1,2} are involved in a team project. If both students devote more effort to the project, they are both better off. Specifically, an effort level is a nonnegative real number, and student 1's payoff function is e₁ (1 + €2-e₁), where e₁ is student 1's effort level, and e2 is student 2's effort level. The cost of effort is higher for student 2 such that her payoff function is given as e2 (1 + 1 - 2e2). (a) Suppose that both students decide their effort levels simultaneously. Find all pure strategy Nash equilibria. (b) Suppose that student 1 decides her effort level first, and after student 2 observes it, she decides her effort level. Find all subgame perfect Nash equilibria, and their outcomes.

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a To find all pure strategy Nash equilibria when both students decide their effort levels simultaneously we need to analyze the best response of each ... View the full answer