Yes I don&#x27;t think this assumption makes a lot of sense in general if you don&#x27;t assume your perfectly rational players have access to randomness (I do think it&#x27;s the best assumption if the players can&#x27;t communicate or have any entropy).<p>In the case of Prisoner&#x27;s Dilemma, if the cooperate&#x2F;defect outcome had sufficiently large cooperation bonus for fixed other payoffs (large enough T&gt;&gt;R in wikipedia&#x27;s notation), then with my assumptions it&#x27;s clear that each prisoner should flip a coin to decide, and each one gets ~T&#x2F;4 expected payoff.<p>But the most glaring problem is of course assuming every player is perfectly rational. Personally I&#x27;d only assume that if your players are all game theorists with enough of time and paper :) I probably wouldn&#x27;t even assume myself as rational.<p>In conclusion, I believe equating maximin with optimal play&#x2F;perfect rationality is misguided, but maximin is a good safe bet.