Suppose there is a joint project that generates an amount 10 for each of the individuals A and B, provided the sum total of A's and B's investments in the project is at least 7. Suppose A's investment is denoted by x and B's by y, where r and y can take any values in {0,1,2,3,4..8,9,10}. A player always has to incur the cost of the investment (equal to æ or y respectively) and gets the benefit if and only if the project goes ahead. Suppose each player is interested in his own net benefit (benefit-cost) and players choose their investment levels simultaneously. The following relate to pure strategies. (a) Is there a Nash equilibrium in which both players invest 0? (b) Is there a Nash equilibrium in which one player invests 0 and the other does not? (c) What is the lowest payoff a player can get in any Nash equilibrium?

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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Suppose there is a joint project that generates an amount 10 for each of the
individuals A and B, provided the sum total of A's and B's investments in the project is
at least 7. Suppose A's investment is denoted by x and B's by y, where r and y can take
any values in {0,1,2,3,4..8,9,10}. A player always has to incur the cost of the investment
(equal to æ or y respectively) and gets the benefit if and only if the project goes ahead.
Suppose each player is interested in his own net benefit (benefit-cost) and players choose
their investment levels simultaneously. The following relate to pure strategies.
(a) Is there a Nash equilibrium in which both players invest 0?
(b) Is there a Nash equilibrium in which one player invests 0 and the other does not?
(c) What is the lowest payoff a player can get in any Nash equilibrium?
Transcribed Image Text:Suppose there is a joint project that generates an amount 10 for each of the individuals A and B, provided the sum total of A's and B's investments in the project is at least 7. Suppose A's investment is denoted by x and B's by y, where r and y can take any values in {0,1,2,3,4..8,9,10}. A player always has to incur the cost of the investment (equal to æ or y respectively) and gets the benefit if and only if the project goes ahead. Suppose each player is interested in his own net benefit (benefit-cost) and players choose their investment levels simultaneously. The following relate to pure strategies. (a) Is there a Nash equilibrium in which both players invest 0? (b) Is there a Nash equilibrium in which one player invests 0 and the other does not? (c) What is the lowest payoff a player can get in any Nash equilibrium?
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