Ex. 5- - Agenda Setting An agenda-setting game is described as follows. The "issue space" (set of feasible poli- cies) is an interval X = [0,5]. An agenda setter (player 1) proposes an alternative x = X against the status quo q = 4. After player 1 proposes x, the legislator (player 2) ob- serves the proposal and selects between the proposal x and the status quo q. Player 1's most-preferred policy is 1, and for any final policy y = X his payoff is given by v1(y) = 10|y — 1|, - where |y1| denotes the absolute value of (y-1). Player 2's most preferred policy is 3, any final policy y Є X he payoff is given by and for v2(y) = 10|y3|. That is, each player prefers policies that are closer to his/her most-preferred policy. (1) Write down the strategic-form representation of the dynamic game. (2) Find a subgame perfect Nash equilibrium. Is it unique?
Ex. 5- - Agenda Setting An agenda-setting game is described as follows. The "issue space" (set of feasible poli- cies) is an interval X = [0,5]. An agenda setter (player 1) proposes an alternative x = X against the status quo q = 4. After player 1 proposes x, the legislator (player 2) ob- serves the proposal and selects between the proposal x and the status quo q. Player 1's most-preferred policy is 1, and for any final policy y = X his payoff is given by v1(y) = 10|y — 1|, - where |y1| denotes the absolute value of (y-1). Player 2's most preferred policy is 3, any final policy y Є X he payoff is given by and for v2(y) = 10|y3|. That is, each player prefers policies that are closer to his/her most-preferred policy. (1) Write down the strategic-form representation of the dynamic game. (2) Find a subgame perfect Nash equilibrium. Is it unique?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![Ex. 5-
- Agenda Setting
An agenda-setting game is described as follows. The "issue space" (set of feasible poli-
cies) is an interval X = [0,5]. An agenda setter (player 1) proposes an alternative x = X
against the status quo q = 4. After player 1 proposes x, the legislator (player 2) ob-
serves the proposal and selects between the proposal x and the status quo q. Player 1's
most-preferred policy is 1, and for any final policy y = X his payoff is given by
v1(y) = 10|y — 1|,
-
where |y1| denotes the absolute value of (y-1). Player 2's most preferred policy is 3,
any final policy y Є X he payoff is given by
and for
v2(y) = 10|y3|.
That is, each player prefers policies that are closer to his/her most-preferred policy.
(1) Write down the strategic-form representation of the dynamic game.
(2) Find a subgame perfect Nash equilibrium. Is it unique?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2e18450-2247-4014-9098-412d609286b8%2F55859f3b-7455-4e17-84d5-3bd8c6a67a81%2Fmc5gtz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ex. 5-
- Agenda Setting
An agenda-setting game is described as follows. The "issue space" (set of feasible poli-
cies) is an interval X = [0,5]. An agenda setter (player 1) proposes an alternative x = X
against the status quo q = 4. After player 1 proposes x, the legislator (player 2) ob-
serves the proposal and selects between the proposal x and the status quo q. Player 1's
most-preferred policy is 1, and for any final policy y = X his payoff is given by
v1(y) = 10|y — 1|,
-
where |y1| denotes the absolute value of (y-1). Player 2's most preferred policy is 3,
any final policy y Є X he payoff is given by
and for
v2(y) = 10|y3|.
That is, each player prefers policies that are closer to his/her most-preferred policy.
(1) Write down the strategic-form representation of the dynamic game.
(2) Find a subgame perfect Nash equilibrium. Is it unique?
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