Question

game theory

4. 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 1,000 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 88 a pound and the large vessel will catch 4,000 pounds of crab and the small vessel 2,500 pound of crab (because they fish at different distances off-shore). 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. (a) Construct a payoff matrix for this game and use it to identify which type of game the fishing firms are playing, (b) What is the basic problem that the two fishing firms face?

Answer 1

4.

a)

Cost of small vessel: $10,000

Cost of large vessel: $20,000

If both have small vessel:

Catch per person: 1000 pounds

Market price: $10 per pound

Total revenue per person: 1000*10=10,000

Total profit per person (Rev-Cost): 10,000-10,000 = 0

If both have large vessel:

Catch per person: 3500 pounds

Market price: $2 per pound

Total revenue per person: 3500*2=7,000

Total profit per person (Rev-Cost): 7,500-20,000 = -12,500

If one has large one has small:

Market price: $8

Catch for the person with small vessel: 2,500

Revenue of the person with small vessel: 2,500*8=20,000

Profit of the person with small vessel: 20,000-10,000=10,000

Catch for the person with large vessel: 4,000

Revenue of the person with large vessel: 4,000*8=32,000

Profit of the person with large vessel: 32,000-20,000=12,000

Using these, we make a matrix

	Small	Large
Small	0;0	10,000; 12,000
Large	12,000;10,000	-12,500;-12,500

This is an example of a non-cooperative game if both fishermen do what's is best for them.

If the two collude, then its a co-operative game

b)

Here, the basic problem is that the maximum profit a fisherman can attain is if he uses a large vessel and the other person uses a small vessel.

If they try to think of the maximum attainable profit, they will both hope that the other person gets a small vessel, they will both get a large vessel and end up making losses.

c)

If one person could commit to a size, say small/large, and stands by it, the other fisherman could get a large/small vessel. Here, one would get 10,000 whereas the other would get 12,000 depending on who has committed to what size. These profits are higher than what they would have gotten if each had gotten a small vessel or if each had gotten a large vessel.

d)

If both people decide to share catch, and one gets a small vessel while the other one gets a large person, the total catch would be 6,500. The total revenue would be 52,000 and each person would get 26,000 each.

The profit of the fisherman with the small vessel would be 26,000-10,000=16,000

The profit of the fisherman with the large vessel would be 26,000-10,000=6,000

Here, the profit of the fisherman with the large vessel is lower compared to the case where he wouldn't share (12,000) but the profit of the small vessel fisherman would be larger compared to the non-sharing case (10,000).

In such a situation, both fishermen would end up getting a small vessel and make 0 profits each.

This situation can work if and only if there are infinitely repeated interactions between them.