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Will_Sawin comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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I found situation where PrudentBot behaves suboptimally and a more intelligent agent can do better. I'm considering an opponent I call pseudo tit-for-tat at level N, or PsTitTatBot[N]. PsTitTatBot[0] is simply CooperateBot. For N>0, the strategy for PsTitTatBot[N] is to simulate its opponent running against PsTitTatBot[N-1], and do the same thing its opponent did in the simulation. PrudentBot would have an outcome of (D,D) against PsTitTatBot[N] for any N. However, it's easy for an agent to ensure that against sufficiently high level tit-for-tat agent the outcome will be (C,C). To do this, there must be a specific N such that this agent plays suboptimally against PsTitTatBot[N]. However, the benefit of mutual cooperation at higher levels should compensate for that.
One simple way to study this is the game where one player chooses PsTitTatBot[N] for some N, and another player chooses any bot. Since this game has an infinite number of strategies, Nash equilibria are poorly behaved. Still, complete mutual cooperation occurs in some Nash equilibria. I have not completely studied which other possibilities can occur.