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?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
18, 21, 45, 138, 555, ?
5 6 15 40 89 170 ?
...45, ?, 84, 114, 151, 195
98, 89, 114, 50, 194, ?
What will come in place of the question mark (?) in the following series?
18, 22, 34, 70, 178, ?
What will come in place of the question mark (?) in the following series?
60, 94, 184, 464, 1388, ?
24, 168, 28, 140, 35, ?Â
12, 18, 30, 54, ?, 198
36   37    33   42    ?      51    15
...26, 227, 628, 1229, ?, 3031
