Invasion by a Tit-for-Tat Minority

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Switching Sides: Tit-for-Tat Minority in a World of Meanies

As we saw in some of the previous slides, greater territorial structure lowers the odds of a successful invasion initiated by a single ever-defecting country on our Toroidal planet. Now we switch sides, and ask the question: how does territorial structure affect the odds of an invasion by a Tit-for-Tat minority?

Firstly, we must realize that a single Tit-for-Tat country would always switch over to All-Defection on a planet otherwise populated by All-D's. Recall the demonstration in Topic 2, Slide 4. There we saw that a Tit-for-Tat agent always gets a lower score than an All-D agent in an interaction between the two, no matter how high the shadow of the future. As a result, all the interaction partners of a Tit-for-Tat country would get higher scores during the first generation, and the country would just have to learn to be mean in a world of meanies.

However, as Axelrod points out in the "Evolution of Cooperation", an invasion by Tit-for-Tats can be made possible under the following conditions:
1. we introduce more than one Tit-for-Tat agent;
2. the percentage of interactions by each Tit-for-Tat agent with other Tit-for-Tats is high enough.

In the next slide we offer one way to confirm and intuit this proposition.

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