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This is an extension of the previous exercise. Consider the following stage game between a manager (also called the "Principal") and a worker (the "Agent").
Let the manager be player 1 and the worker be Player 2. Simultaneously, the manager chooses a bonus payment p E [0, x) and the worker chooses an effort level a E [0, co). The stage-game payoffs are
u1(p, a) = 4a - p and u2(p, a) = p - a2.
(a) Determine the efficient effort level for the worker.
(b) Find the Nash equilibrium of the stage game.
(c) Suppose the stage game is to be played twice (a two-period repeated game) and there is no discounting. Find all of the subgame perfect equilibria.
(d) Suppose the stage game is to be played infinitely many times in succession (an infinitely repeated game) and assume that the players share the discount factor 6 < 1. Find conditions on the discount factor under which there is a subgame perfect equilibrium featuring selection of the efficient effort level in each period (on the equilibrium path).
Verified Expert
The Nash Equilibrium is about the game theory where two players participate in the game. The employer and the employee play a major role in the game. The question is all about what the employee can do within the work setup. The more the employee puts more effort in working, the more he/she gets the yield from the employer.
Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.
A supplier and a buyer, who are both risk neutral, play the following game, The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
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Determine the solution to the given advertising decision game between Coke and Pepsi, assuming the companies act independently.
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Suppose you and your classmate are assigned a project on which you will earn one combined grade. You each wish to receive a good grade, but you also want to avoid hard work.
Consider trade relations in the United State and Mexico. Suppose that leaders of two countries believe the payoffs to alternative trade policies are as follows:
Use the given payoff matrix for a simultaneous move one shot game to answer the accompanying questions.
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