Consider the following simple model of a cocktail party. Alice and Bob are carrying on separate conversations at the party. Alice speaks at volume a and Bob speaks at volume b. The communicatio al(a + b) and the benefit to Bob is b/(a + b). The vocal-strain cost to Alice is ca and the cost to Bob is cb, where c is a parameter. Suppose that the players have two choices: speaking softly at volume 1, or speaking loudly at volume 4. This leads to the following game in s Alice choosing the row and Bob choosing the column.
Consider the following simple model of a cocktail party. Alice and Bob are carrying on separate conversations at the party. Alice speaks at volume a and Bob speaks at volume b. The communicatio al(a + b) and the benefit to Bob is b/(a + b). The vocal-strain cost to Alice is ca and the cost to Bob is cb, where c is a parameter. Suppose that the players have two choices: speaking softly at volume 1, or speaking loudly at volume 4. This leads to the following game in s Alice choosing the row and Bob choosing the column.
Chapter1: Making Economics Decisions
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![THE PRISONERS' DILEMMA
Consider the following simple model of a cocktail party.
Alice and Bob are carrying on separate conversations at the party. Alice speaks at volume a and Bob speaks at volume b. The communication benefit to Alice is
al(a + b) and the benefit to Bob is b/(a + b). The vocal-strain cost to Alice is ca and the cost to Bob is cb, where c is a parameter.
Suppose that the players have two choices: speaking softly at volume 1, or speaking loudly at volume 4. This leads to the following game in strategic form, with
Alice choosing the row and Bob choosing the column.
a = 1
a = 4
b = 1
0.5-c, 0.5-c
0.8-4c, 0.2-c
0.0400
0.0500
0.0750
0.0800
0.1500
b = 4
0.2 c, 0.8-4c
-
0.54c, 0.5-4c
For which of the following values of c is this game a prisoners' dilemma? (Mark all values for which this is true.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35bc7cfb-e38c-45d6-8cb2-8c987ddfb016%2Fd3ff2955-3d13-4cea-ad25-1851779a3417%2Fi4vap9h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:THE PRISONERS' DILEMMA
Consider the following simple model of a cocktail party.
Alice and Bob are carrying on separate conversations at the party. Alice speaks at volume a and Bob speaks at volume b. The communication benefit to Alice is
al(a + b) and the benefit to Bob is b/(a + b). The vocal-strain cost to Alice is ca and the cost to Bob is cb, where c is a parameter.
Suppose that the players have two choices: speaking softly at volume 1, or speaking loudly at volume 4. This leads to the following game in strategic form, with
Alice choosing the row and Bob choosing the column.
a = 1
a = 4
b = 1
0.5-c, 0.5-c
0.8-4c, 0.2-c
0.0400
0.0500
0.0750
0.0800
0.1500
b = 4
0.2 c, 0.8-4c
-
0.54c, 0.5-4c
For which of the following values of c is this game a prisoners' dilemma? (Mark all values for which this is true.)
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