Two fishing firms, Seafood Unlimited and Critter Catchers, catch Dungeness Crab off the Oregon coast. Each chooses between using…

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Two fishing firms, “Seafood Unlimited” and “Critter Catchers,” catch Dungeness Crab off

the Oregon coast. Each chooses between using a large vessel or a small one. It costs $10,000

and $20,000 to run a small and large vessel, respectively, for a fishing season. If both run small

vessels, they will each catch 2,500 pounds of crab per season, and the market price will be $10

a pound. If one uses a small vessel and the other a large one, the market price will be $8, and

the large vessel will catch 4,000 pounds of crab and the small vessel 2,500 pounds of crab

(because they fish at different distances offshore). If both choose large vessels, they will both

catch 3,500 pounds of crab, and the market price of crab will be $2. The fishing firms must

make their vessel size choices simultaneously. Firms measure their utility in profit. Recall profit

= revenue – cost. (Dr. Ellis, University of Oregon)

a. Specify: players, strategies

b. Construct a payoff matrix for this game

c. Find pure strategy Nash equilibrium

d. Give both definitions of a Nash equilibrium

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