Partnership Game Lee (Player 1), and Julie (Player 2), are business partners. Each of them has to determine the amount of effort he or she will put into the business, which is denoted by ei, i = 1,2, and may be any nonnegative real number: The cost of effort ei for Player i is cei, where c> 0 is equal for both players. The success of the business depends on the amount of effort put in by the players. The business's profit is denoted by (e1,e2) = elae2a, where a € (0, 1) is a fixed constants known by Lee and Julie, and the profit is shared equally between the two partners. Each player's utility is given by the difference between the share of the profit received by that player and the cost of the effort he or she put into the business. Answer the following questions: (a) Describe this situation as a strategic-form game. Note that the set of strategies of each player is the continuum. (b) Find all the Nash equilibria of the game. (c) Find the efficient solution of the game and compare it to the Nash equilibrium.

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Chapter1: Making Economics Decisions
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Partnership Game
Lee (Player 1), and Julie (Player 2), are business partners. Each of them has to determine the amount
of effort he or she will put into the business, which is denoted by ei, i = 1,2, and may be any
nonnegative real number: The cost of effort ei for Player i is cei, where c > 0 is equal for both
players. The success of the business depends on the amount of effort put in by the players. The
business's profit is denoted by n(e1,e2) = elae2a, where a E (0, 1) is a fixed constants known by Lee
and Julie, and the profit is shared equally between the two partners. Each player's utility is given by
the difference between the share of the profit received by that player and the cost of the effort he
or she put into the business. Answer the following questions:
(a) Describe this situation as a strategic-form game. Note that the set of strategies of each player is
the continuum.
(b) Find all the Nash equilibria of the game.
(C) Find the efficient solution of the game and compare it to the Nash equilibrium.
Transcribed Image Text:Partnership Game Lee (Player 1), and Julie (Player 2), are business partners. Each of them has to determine the amount of effort he or she will put into the business, which is denoted by ei, i = 1,2, and may be any nonnegative real number: The cost of effort ei for Player i is cei, where c > 0 is equal for both players. The success of the business depends on the amount of effort put in by the players. The business's profit is denoted by n(e1,e2) = elae2a, where a E (0, 1) is a fixed constants known by Lee and Julie, and the profit is shared equally between the two partners. Each player's utility is given by the difference between the share of the profit received by that player and the cost of the effort he or she put into the business. Answer the following questions: (a) Describe this situation as a strategic-form game. Note that the set of strategies of each player is the continuum. (b) Find all the Nash equilibria of the game. (C) Find the efficient solution of the game and compare it to the Nash equilibrium.
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