New One Goal, Three Exams: Strategies for Mastering RBI, SEBI, and IFSCA Exams
Register

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?

A (n+1)2 Correct Answer Incorrect Answer
B n2 Correct Answer Incorrect Answer
C [6000 / (n+1)]2 Correct Answer Incorrect Answer
D [2000 / (n+1)]2 Correct Answer Incorrect Answer
E Can’t say Correct Answer Incorrect Answer

Solution

Fish caught by “i”: a i (2000- (a i + Σ j≠i a j )). Now we have to maximise this expression. Therefore differentiating w.r.t ai and equating to 0 a i = 1000 - Σ j≠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

Practice Next
×
×