2. An agent can pursue activity A or activity B. Activity B yields the return 0. Activity A yields the return y but requires both an unrecoverable investment of c, where 0

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Chapter1: Making Economics Decisions
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2. An agent can pursue activity A or activity B. Activity B yields the return 0. Activity
A yields the return y but requires both an unrecoverable investment of c, where
0 < c < y, and a permit from an official. The permit is free, but the official may
demand a bribe of any magnitude; the permit is granted only after the investment
has been made and the bribe paid.
(a) Model this situation as an extensive game with perfect information in which the
agent first chooses A or B. If she chooses B, the game ends and her payoff and
that of the official are both 0. If she chooses A, the official then demands a
bribe (any number), which the agent either agrees or refuses to pay. If the agent
agrees to pay the bribe, she pursues activity A and her payoff is y-c-b while
the official's payoff is b, where b is the bribe demanded by the official. If the
agent refuses to pay the bribe, her payoff is -c and that of the official is 0.
(b) Find the subgame perfect equilibrium/equilibria of the game.
Transcribed Image Text:2. An agent can pursue activity A or activity B. Activity B yields the return 0. Activity A yields the return y but requires both an unrecoverable investment of c, where 0 < c < y, and a permit from an official. The permit is free, but the official may demand a bribe of any magnitude; the permit is granted only after the investment has been made and the bribe paid. (a) Model this situation as an extensive game with perfect information in which the agent first chooses A or B. If she chooses B, the game ends and her payoff and that of the official are both 0. If she chooses A, the official then demands a bribe (any number), which the agent either agrees or refuses to pay. If the agent agrees to pay the bribe, she pursues activity A and her payoff is y-c-b while the official's payoff is b, where b is the bribe demanded by the official. If the agent refuses to pay the bribe, her payoff is -c and that of the official is 0. (b) Find the subgame perfect equilibrium/equilibria of the game.
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