Problem 1. Is the following function P an exact potential for Prisoner's Dilemma? Justify your answer. Player 2 Quiet Fink Quiet Fink Quiet Fink Quiet Fink 2, 2 0,3 1 Player 1 3,0 1,1 1 2 Prisoner's Dilemma Function P

Microeconomics: Principles & Policy
14th Edition
ISBN:9781337794992
Author:William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:William J. Baumol, Alan S. Blinder, John L. Solow
Chapter13: Between Competition And Monopoly
Section: Chapter Questions
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Tutorial 3 - Questions
Problem 1. Is the following function P an exact potential for Prisoner's Dilemma? Justify your answer.
Player 2
Quiet
Fink
2, 2
0,3
3,0
1,1
Quiet
Fink
Quiet
Fink
Quiet
Fink
1
Player 1
Prisoner's Dilemma
Function P
Problem 2. Is the following function P' a weighted potential for Prisoner's Dilemma? Justify your answer.
Quiet
Fink
Quiet
Fink
1
2
3
Function P'
Problem 3. In the following congestion game, where n players (n > 6) can use three edges to go from A to B
(1 edge each):
(a) What would be the maximum value of the Rosenthal Potential?
(b) What is the value of the Rosenthal Potential when the players split equally to the three edges? (Assume
n is divisible by 3.)
(c) What is the worst-case running time of the algorithm (from lecture notes) for finding a PNE?
3r +2
A
т — 5
II
Transcribed Image Text:Tutorial 3 - Questions Problem 1. Is the following function P an exact potential for Prisoner's Dilemma? Justify your answer. Player 2 Quiet Fink 2, 2 0,3 3,0 1,1 Quiet Fink Quiet Fink Quiet Fink 1 Player 1 Prisoner's Dilemma Function P Problem 2. Is the following function P' a weighted potential for Prisoner's Dilemma? Justify your answer. Quiet Fink Quiet Fink 1 2 3 Function P' Problem 3. In the following congestion game, where n players (n > 6) can use three edges to go from A to B (1 edge each): (a) What would be the maximum value of the Rosenthal Potential? (b) What is the value of the Rosenthal Potential when the players split equally to the three edges? (Assume n is divisible by 3.) (c) What is the worst-case running time of the algorithm (from lecture notes) for finding a PNE? 3r +2 A т — 5 II
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