Question
Suppose there is a pond with fishes and βnβ 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- Ξ£ i a i ). The number of fish caught by a fisherman βjβ is: a j (2000- Ξ£ i a i ). Then what would be the best response of fisherman βiβ to maximise his total?Solution
Fish caught by βiβ: a i (2000- (a i + Ξ£ jβ i a j )). Now we have to maximise this expression. Therefore differentiating w.r.t ai and equating to 0 a i = 1000 - Ξ£ jβ i 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 / (n+1) So catch by each player=[2000 / (n+1)] 2
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