Question

Suppose there is a pond with fishes and “n” number of fishermen living around it. Let a i is time spent fishing per day by player
i. Thus total time per day is a 1 + ... + a n. The number of fish available at any time is given by: (2000- Σ i a i ). The number of fish caught by a fisherman “j” is: a j (2000- Σ i a i ). Then what would be the best response of fisherman “i” to maximise his total?

Q: Answer-Suppose there is a pond with fishes and “n” number of fishermen living around it. Let a i is time sp...

Fish caught by i a i 2000- a i ji a j . Now we have to maximise this expression. Therefore differentiating w.r.t ai and equating to 0 a i 1000 - ji a j 2 Now each player will try to maximise his catch and assuming each one using the same strategy a i a to achieve equilibrium a 1000 - n-1 a 2 a 2000 n1 So catch by each player2000 n1 2