Stability of defection, optimisation of strategies and the limits of memory in the Prisoner's Dilemma
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Memory-one strategies are a set of Iterated Prisoner's Dilemma strategies that have been acclaimed for their mathematical tractability and performance against single opponents. This manuscript investigates best responses to a collection of memory-one strategies as a multidimensional optimisation problem. Though extortionate memory-one strategies have gained much attention, we demonstrate that best response memory-one strategies do not behave in an extortionate way, and moreover, for memory one strategies to be evolutionary robust they need to be able to behave in a forgiving way. We also provide evidence that memory-one strategies suffer from their limited memory in multi agent interactions and can be out performed by longer memory strategies.
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