(1) suppose a worker is hired to by an employer to work at a large car...
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(1) suppose a worker is hired to by an employer to work at a large car company. There are two types of workers: selfish (S) and cooperators (C). There is only one type of employer. The employer does not the type of worker but knows that 2/5 of workers are selfish and 3/5 are cooperators. The workers know their type. This situation is represented by the following game: Type=C Employer High Pay Low Pay Don't Pay High Effort 5,5 0,3 -2,4 Worker Low Effort 1,0 2,2 -1,3 Type S Employer High Pay Low Pay Don't Pay High Effort 5,5 0,3 -3,4 Worker Low Effort 6,0 2,2 -1,2 ) Draw the ex-ante game. High Pay High if C, High if S 5,5 High if C Low if S Low if C, High if S Low if C, Low if S 3/5(1+2/5(6), 0 Employer Low Pay 0,3 Don't pay 3/5(-2)=2/5(-3), 4 3/5(52/5(6), 3/5(5)+2/5(0) | 3/5(02/5(2), 3/5(3)+2/5(2) || 3/5(-2)=2/5(-1), 3/5(4)+2/5(2) 3/5(12/5(5), 3/5(0)+2/5(5) 3/5(22/5(0), 3/5(2)+2/5(3) 3/5(-12/5(-3), 3/5(3)+2/5(4) 2,2 -1, 3/5(3)+2/5(2) Employer High Pay Low Pay Don't pay High if C, 5,5 0,3 High if S High if C, 12/5, 3 4/5, 13/5 -12/5,4 -8/5, 15/5 Low if S Low if C, 13/5, 2 6/5, 12/5 -9/5, 17/5 High if S Low if C, Low if S 3,0 2,2 -1, 13/5 Find all (if any) pure strategy Bayesian Nash Equilibrium in the game (a). High if C, High if S High Pay 5,5 Low Pay 0,3 High if C, 12/5,3 4/5, 13/5 Low if S Don't pay -12/5,4 -8/5, 16/5 Low if C, 13/5, 2 6/5, 12/5 High if S -9/5, 17/5 Low if C, 3,0 2,2 -1, 13/5 Low if S We have one pure Bayesian Nash equilibrium {Low if C, Low if Don't pay) Workers' Strategy Employer's Strategy (1) suppose a worker is hired to by an employer to work at a large car company. There are two types of workers: selfish (S) and cooperators (C). There is only one type of employer. The employer does not the type of worker but knows that 2/5 of workers are selfish and 3/5 are cooperators. The workers know their type. This situation is represented by the following game: Type=C Employer High Pay Low Pay Don't Pay High Effort 5,5 0,3 -2,4 Worker Low Effort 1,0 2,2 -1,3 Type S Employer High Pay Low Pay Don't Pay High Effort 5,5 0,3 -3,4 Worker Low Effort 6,0 2,2 -1,2 ) Draw the ex-ante game. High Pay High if C, High if S 5,5 High if C Low if S Low if C, High if S Low if C, Low if S 3/5(1+2/5(6), 0 Employer Low Pay 0,3 Don't pay 3/5(-2)=2/5(-3), 4 3/5(52/5(6), 3/5(5)+2/5(0) | 3/5(02/5(2), 3/5(3)+2/5(2) || 3/5(-2)=2/5(-1), 3/5(4)+2/5(2) 3/5(12/5(5), 3/5(0)+2/5(5) 3/5(22/5(0), 3/5(2)+2/5(3) 3/5(-12/5(-3), 3/5(3)+2/5(4) 2,2 -1, 3/5(3)+2/5(2) Employer High Pay Low Pay Don't pay High if C, 5,5 0,3 High if S High if C, 12/5, 3 4/5, 13/5 -12/5,4 -8/5, 15/5 Low if S Low if C, 13/5, 2 6/5, 12/5 -9/5, 17/5 High if S Low if C, Low if S 3,0 2,2 -1, 13/5 Find all (if any) pure strategy Bayesian Nash Equilibrium in the game (a). High if C, High if S High Pay 5,5 Low Pay 0,3 High if C, 12/5,3 4/5, 13/5 Low if S Don't pay -12/5,4 -8/5, 16/5 Low if C, 13/5, 2 6/5, 12/5 High if S -9/5, 17/5 Low if C, 3,0 2,2 -1, 13/5 Low if S We have one pure Bayesian Nash equilibrium {Low if C, Low if Don't pay) Workers' Strategy Employer's Strategy
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