Agent Strategies and the Shadow of the Future

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Choice of a Strategy Function

In the last slide a Tit-for-Tat interacted with an All-D as the shadow of the future parameter δ was set to 1/2. Tit-for-Tat was not doing too well, since she kept forgetting All-D's last defection every few moves. Clearly, she would have benefited from a greater influence of the shadow of the future, which would have insured a higher percentage of 1-point instead of 0-point payoffs.

What about the All-D agent, though? Was it most advantageous for her to stick to the All-D strategy? Or would she have benefited from switching to her opponent's Tit-for-Tat strategy instead? For even though she got the exorbitant 5-point payoff from time to time, the rest of the time she got a meager mutual defection point. If she were to switch to a Tit-for-Tat strategy, however, she would get the steady 3-point mutual cooperation payoffs.

As we will see in the next slide, the answer to this question depends greatly on δ. This will hardly come as a surprise, since the parameter affects the percentage of 1-point payoffs an All-D agent suffers.

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