Strategy23Handout - 12/2/2008 Collective Action Games N =...

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12/2/2008 1 Collective Action Games ± N = population ± n = # of participants who take an action ± N-n = # of shirkers who do not take the action ± Participant gets: p(n) ± Shirker gets: s(n) Collective Action Games ± Suppose there are n participants and N-n-1 shirkers, and JoJo is trying to decide what to do: ± Participate and get p(n+1) Shirk and get s(n ± Shirk and get s(n) ± Whether to participate or not depends on whether or not p(n+1)>s(n) Career Choice ± There are 1,000 students in a graduating class at Dartmouth College ± n graduates will become doctors ± 1,000 – n will become MBA’s ± Because doctors will stay in New Hampshire ± each doctor’s income is a function of the number of others who choose to be doctors ± p(n) = 250 – n /6 (thousands of dollars) ± MBA’s are hired away to New York ± each MBA’s income is a constant s(n) = 150 (thousand dollars) Career Choice ± Suppose n students have chosen to become doctors, then JoJo would like to become a doctor if ± 250-(n+1)/6 = p(n+1) s(n) = 150 OR ± 599 n ± In equilibrium with free choice, 600 students will choose to become doctors Career Choice Career Choice ± What number of doctors would maximize total class income? ± Dartmouth wants class income maximized to maximize donations to its endowment ± Maximize ± T(n) = n (250 – n /6) + (1,000 – n )150 ± T’(n) = 250 – n/2 – 150 set= 0 ± n* = 300 ± Dartmouth’s optimal number of doctors is only one-half the number that arises in the free choice equilibrium
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12/2/2008 2 Spillovers ± Spillovers cause the maximizing number of participants to differ from the free choice equilibrium ± T(n) = n·p(n) + (N-n)·s(n) ±
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Strategy23Handout - 12/2/2008 Collective Action Games N =...

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