There is a community of 400 commercial fishers, and there are two lakes where they can fish, ONE and TWO. Fishers choose the lake on which they fish. On ONE, the catch per fisher is 30 pounds, regardless of how many fishers choose ONE. On TWO the catch per fisher decreases as the number of fishers increases. Specifically, C2 = 200 – N2, where N2 is the number of fishers on TWO and C2 is pounds of fish caught by each fisher. Fishers' preferences: Fishers care about the quantity of fish they catch, the more they catch, the better off they are. In addition, if a fisher anticipates that the quantity of fish he would catch on ONE is identical to the quantity he would catch on TWO, he prefers to fish on TWO. (a) Why this problem is the Game Theory problem? (b) What is a strategy set for a representative player REP? (c) Let M be the number of fishers other than a representative, REP, who choose to fish on TWO. Construct a payoff table for REP in the game in which all 400 fishers choose a lake, either ONE or TWO. (d) When REP will choose to fish on ONE? When REP will choose to fish on TWO? Explain. (e) In equilibrium, how many fishers fish on ONE and how many fish on TWO? Is this the only Nash equilibrium? What are the fishers' payoffs in these equilibria? (f) Are the Nash equilibria Pareto-optimal? If you think not, pick one of the equilibria and find a strategy combination that Pareto-dominates it - explain where you see Pareto improvement. (g) Graph the payoff functions to find REP's best response function. Dis- cuss your findings.
There is a community of 400 commercial fishers, and there are two lakes where they can fish, ONE and TWO. Fishers choose the lake on which they fish. On ONE, the catch per fisher is 30 pounds, regardless of how many fishers choose ONE. On TWO the catch per fisher decreases as the number of fishers increases. Specifically, C2 = 200 – N2, where N2 is the number of fishers on TWO and C2 is pounds of fish caught by each fisher. Fishers' preferences: Fishers care about the quantity of fish they catch, the more they catch, the better off they are. In addition, if a fisher anticipates that the quantity of fish he would catch on ONE is identical to the quantity he would catch on TWO, he prefers to fish on TWO. (a) Why this problem is the Game Theory problem? (b) What is a strategy set for a representative player REP? (c) Let M be the number of fishers other than a representative, REP, who choose to fish on TWO. Construct a payoff table for REP in the game in which all 400 fishers choose a lake, either ONE or TWO. (d) When REP will choose to fish on ONE? When REP will choose to fish on TWO? Explain. (e) In equilibrium, how many fishers fish on ONE and how many fish on TWO? Is this the only Nash equilibrium? What are the fishers' payoffs in these equilibria? (f) Are the Nash equilibria Pareto-optimal? If you think not, pick one of the equilibria and find a strategy combination that Pareto-dominates it - explain where you see Pareto improvement. (g) Graph the payoff functions to find REP's best response function. Dis- cuss your findings.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:There is a community of 400 commercial fishers, and there are two lakes
where they can fish, ONE and TWO. Fishers choose the lake on which they
fish. On ONE, the catch per fisher is 30 pounds, regardless of how many
fishers choose ONE. On TWO the catch per fisher decreases as the number
of fishers increases. Specifically, C, = 200 – N2, where N, is the number
of fishers on TWO and C2 is pounds of fish caught by each fisher.
Fishers' preferences: Fishers care about the quantity of fish they catch, the
more they catch, the better off they are. In addition, if a fisher anticipates
that the quantity of fish he would catch on ONE is identical to the quantity
he would catch on TWO, he prefers to fish on TWO.
(a) Why this problem is the Game Theory problem?
(b) What is a strategy set for a representative player REP?
(c) Let M be the number of fishers other than a representative, REP, who
choose to fish on TWO. Construct a payoff table for REP in the game
in which all 400 fishers choose a lake, either ONE or TWO.
(d) When REP will choose to fish on ONE? When REP will choose to fish
on TWO? Explain.
(e) In equilibrium, how many fishers fish on ONE and how many fish on
TWO? Is this the only Nash equilibrium? What are the fishers' payoffs
in these equilibria?
(f) Are the Nash equilibria Pareto-optimal? If you think not, pick one of
the equilibria and find a strategy combination that Pareto-dominates it
- explain where you see Pareto improvement.
(g) Graph the payoff functions to find REP's best
cuss your findings.
response
function. Dis-
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