. (10 points) Suppose there is a society of 10 individuals. The individuals need
ID: 1112989 • Letter: #
Question
. (10 points) Suppose there is a society of 10 individuals. The individuals need to work together in order to complete a public works project. Each individual simultaneously and independently chooses whether or not to contribute, e.g., draining a swamp. In order to complete the project, at least 5 individuals must contribute. If the project is completed, each individual receives a benefit of B. Each individual who contributes bears a cost of C. If the project fails, players receive no benefits, but contributing players still bear the costs of contributing. (a) (4 points) Suppose that B C. What is/are the Nash equilibrium/equilibria? Explain. (d) (1 point) Is/are the equilibrium/equilibria found in (e) efficient?Explanation / Answer
a) If n = 1 contribute then there is incentive to deviate to not contribut. Thus not a Nash Equilibrium.
If n= 2 agin incentive to deviate.
.
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N=5 no incentive to deviate.
N=6 incentive to deviate to not contribute and yet receive the benefits. Therefore not a Nash equilibrium.
.
.
Thus the Nash equilibrium is N= 5 where exactly 5 individuals contribute.
b) Yes efficient.
c) B>C the;
N=1 incentive to deviate t not contribute, not Nash equilibrium..
N=2, incentive to deviate to not contribute
N= 3, not a Nash equilibrium incentive to deviate.
N=5 , Nash equilibrium, no incentive to deviate.
N=6, incentive to deviate since the project is completed with the 5 individuals and his payoffs can be increased by not contributing. Thus not a nash equilibrium.
.
.
d)Yes efficient.
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