Microeconomics (2nd Edition) (Pearson Series in Economics)
2nd Edition
ISBN: 9780134492049
Author: Daron Acemoglu, David Laibson, John List
Publisher: PEARSON
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Question
Chapter 13, Problem 9P
(a)
To determine
Player 1’s choice in the second move.
(i) When “green, green” is played.
(ii) When “red, red” is played.
(b)
To determine
Player 2’s choice when:
(i) Player 1 played green.
(ii) Player 1 played red.
(c)
To determine
Player 1’s decision when a choice is made for the first time.
(d)
To determine
Equilibrium path in the game of picking red and green.
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Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 6 and Deborah will receive a payoff of 5.
Deborah
Left
Right
Carlos
Left
8, 4
4, 5
Right
5, 4
6, 5
The only dominant strategy in this game is for to choose .
The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses .
Suppose Yakov and Ana are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows.
the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Yakov chooses Right and Ana
chooses Right, Yakov will receive a payoff of 6 and Ana will receive a payoff of 6.
Yakov
Left
Left
2,3
Right 3,7
Ana
Right
4,4
6,6
The only dominant strategy in this game is for
to choose
The outcome reflecting the unique Nash equilibrium in this game is as follows: Yakov chooses
and Ana chooses
Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
Chapter 13 Solutions
Microeconomics (2nd Edition) (Pearson Series in Economics)
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