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How does species co-survive? A game theoretic perspective
How do populations of different species survive over time? Under what conditions do they co-exist and when do they dominate the other one?
Evolutionary game theory is a special branch of game theory, which adds a dimension of “time” to the world of pay-off matrices. Before diving deeper into the evolution aspect, let me give you a brief of Game Theory itself. In game theory, each player has a set of strategies. The pay-off matrix determines what the outcome is going to be if each player chooses a strategy. One of the most famous examples is the “Prisoner’s Dilemma”. Here there are two prisoners in custody, each separated and have no way to communicate. Officers give each prisoner the same three offers: testify against the other and you go free and the other person goes to jail for 3 years; if both the prisoners stay silent, they each go to jail for 1 year; if both testify against each other, they each go to jail for 2 years. Given no way to communicate, for each rational prisoner, the best course of action is to testify against the other. Why? Given that prisoner A doesnt know what they are going to do, he has to evaluate his options. If B chooses to stays silent, A knows that his best strategy is to testify, because then he walks away with no jail time. If B chooses to testifies against A, A knows that if he is silent he will go to jail for 3 years, and if he also testifies he goes to jail for 2 years. So whatever B does, A has a dominant strategy to always testify agaisnt B. Same way for B, he also reasons that testifying against A is his best strategy. The fun part about this dilemma is that, both choose to testify against each other and go to jail for 2 years each. However, on retrospect, if both had stayed silent, they would each go to jail for 1 year each, a significantly better outcome for both. “Prisoner’s Dilemma” shows that in a society of independant people who think about their best, cooperation for the greater good almost never happens.
