Agent Learning and Strategy Invasion

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Effect of the Territorial Structure

You might have noticed in the previous slide that Tit-for-Tats were better at resisting the invasion for higher values of α. Why would this tend to happen? Essentially, because when the territorial structure is high, most of the Tit-for-Tats start off interacting only with other Tit-for-Tats. As a result, they maintain high total payoffs, and serve as role models for the neighbors that were unfortunate enough to be exploited by an All-D agent. On the other hand, when there is little territorial structure, the All-D agent weakens a large number of Tit-for-Tat agents during the first generation, which increases the probability that some of them will see All-D as the most successful strategy around.

To confirm the above intuition, we set up and ran the following experiment. α varied from 0 (no territorial structure) to 10 (high degree of territorial structure). For each α, 300 societies such as the one in the previous slide were created and run for 300 steps. Below, we plot the ratio of the number of societies where All-D strategy successfully took over the entire society to the number of societies where it was completely wiped out by step 300.

Figure 1. Ratio of completed All-D invasions to repelled All-D invasions. δ = 0.5

As you can see, Tit-for-Tats got better and better at dealing with the invading strategy as the territorial structure increased, just as we predict at the top of the slide.

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