Yes I don't think this assumption makes a lot of sense in general if you don't assume your perfectly rational players have access to randomness (I do think it's the best assumption if the players can't communicate or have any entropy).
In the case of Prisoner's Dilemma, if the cooperate/defect outcome had sufficiently large cooperation bonus for fixed other payoffs (large enough T>>R in wikipedia's notation), then with my assumptions it's clear that each prisoner should flip a coin to decide, and each one gets ~T/4 expected payoff.
But the most glaring problem is of course assuming every player is perfectly rational. Personally I'd only assume that if your players are all game theorists with enough of time and paper :) I probably wouldn't even assume myself as rational.
In conclusion, I believe equating maximin with optimal play/perfect rationality is misguided, but maximin is a good safe bet.
In the case of Prisoner's Dilemma, if the cooperate/defect outcome had sufficiently large cooperation bonus for fixed other payoffs (large enough T>>R in wikipedia's notation), then with my assumptions it's clear that each prisoner should flip a coin to decide, and each one gets ~T/4 expected payoff.
But the most glaring problem is of course assuming every player is perfectly rational. Personally I'd only assume that if your players are all game theorists with enough of time and paper :) I probably wouldn't even assume myself as rational.
In conclusion, I believe equating maximin with optimal play/perfect rationality is misguided, but maximin is a good safe bet.