* Consider N=10 individuals using a public lake for fishing; * At the beginning of each turn individuals decide on the number of fishing rods to use, s(i); * At the end of each turn individuals receive *|f(i)=s(i).(1-Stot/400)|*, where Stot is the total number of fishing rods used by all individuals and K=400 is the fishing capacity of the lake. At the beginning of the each turns individuals choose s(i) as follows, * Given previous turn's Stot, the individual considers if adding one more fishing rod would give him more fish, if *|f(y)=(s(i)+1).(1-(Stot+1)/400)>f(i)|*, individual uses in the next turn s(i)+1 fishing rods,otherwise s(i) kept constant. How can I write a program to simulate the above situation for T=100 turns, starting with s(i)=0? And how can plot individuals' fishing results f(i) as function of time?

Tragedy of the Commons Question on MATLAB

19 Dec 2014

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Consider N=10 individuals using a public lake for fishing;
At the beginning of each turn individuals decide on the number of fishing rods to use, s(i);
At the end of each turn individuals receive f(i)=s(i).(1-Stot/400), where Stot is the total number of fishing rods used by all individuals and K=400 is the fishing capacity of the lake.

At the beginning of the each turns individuals choose s(i) as follows,

Given previous turn's Stot, the individual considers if adding one more fishing rod would give him more fish, if f(y)=(s(i)+1).(1-(Stot+1)/400)>f(i), individual uses in the next turn s(i)+1 fishing rods,otherwise s(i) kept constant.

How can I write a program to simulate the above situation for T=100 turns, starting with s(i)=0?

And how can plot individuals' fishing results f(i) as function of time?