N residents witness a fire in a building. Each resident can independently choose to help or not. As long as someone helps, the fire is extinguished and every resident gets a benefit of b = 5. However, any resident stopping to help pays a personal cost of c = 4, due to the possible injury. If no resident helps the fires causes damage to the building, and the payoff to all players is 0. That is, if a player decides to help, her payoff is 5-4 = 1; if she does not help and at least one of the other residents helps, her payoff is 5; and, if she does not help and neither do the other residents, her payoff is 0. Solve for the symmetric mixed strategy Nash equilibrium when N = 2. What is the probability that at least one resident stops to help? Hint: The probability that at least one player stops to help is equal to the probability that either of the players stops to help or that both players stop to help. A convenient way of computing this probability is one minus the probability that none of the players stops to help. (a) 0.06 (b) 0.16 (c) 0.2 (d) 0.36

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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N residents witness a fire in a building. Each resident can independently choose to help
or not. As long as someone helps, the fire is extinguished and every resident gets a benefit
of b = 5. However, any resident stopping to help pays a personal cost of c = 4, due to the
possible injury. If no resident helps the fires causes damage to the building, and the payoff
to all players is 0.
That is, if a player decides to help, her payoff is 5 - 4 = 1; if she does not help and at
least one of the other residents helps, her payoff is 5; and, if she does not help and neither
do the other residents, her payoff is 0.
Solve for the symmetric mixed strategy Nash equilibrium when N = 2. What is the
probability that at least one resident stops to help?
Hint: The probability that at least one player stops to help is equal to the probability
that either of the players stops to help or that both players stop to help. A convenient
way of computing this probability is one minus the probability that none of the
players stops to help.
(a) 0.06
(b) 0.16
(c) 0.2
(d) 0.36
Transcribed Image Text:N residents witness a fire in a building. Each resident can independently choose to help or not. As long as someone helps, the fire is extinguished and every resident gets a benefit of b = 5. However, any resident stopping to help pays a personal cost of c = 4, due to the possible injury. If no resident helps the fires causes damage to the building, and the payoff to all players is 0. That is, if a player decides to help, her payoff is 5 - 4 = 1; if she does not help and at least one of the other residents helps, her payoff is 5; and, if she does not help and neither do the other residents, her payoff is 0. Solve for the symmetric mixed strategy Nash equilibrium when N = 2. What is the probability that at least one resident stops to help? Hint: The probability that at least one player stops to help is equal to the probability that either of the players stops to help or that both players stop to help. A convenient way of computing this probability is one minus the probability that none of the players stops to help. (a) 0.06 (b) 0.16 (c) 0.2 (d) 0.36
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