Eugene:
Lucifer:
PD is also alleged to be an accurate description of rational behavior in multiple but finite repeated games where each player knows the number of times it's played.
Well, that is true. So one-offs and a finite, known string of one-offs.... 
PD is not a description of behavior at all, it is an environment in which two agents act and receive a reward.
There's a concept (sorry if you already know this) called "Nash Equilibrium" which is the result of evaluting the current state and chaging your action if doing so will put you into a better state. The Nash Equilibrium for PD is both people betraying each other (to reach this conclusion, all you have to do is pick a spot in the PD grid and ask if either player can better their position by changing their action--the only place that they cannot do this is when both defect).
This has absolutely nothing to do with any decisions made by any person. It's a mathematical/game-theoretic construct with an interesting property.
In a string of PD games, the optimal strategy is tit-for-tat. I cooperate until you defect then I defect once for each time you do. Then I continue to cooperate. Robert Axelrod wrote a number of books/articles on the subject that discuss the advantages of cooperation based on his work in multi-agent decsions making (which touches game theory quite alot).
In any case, the guy in the video isn't even talking about PD, and PD has not ever, in any way, been contrued to necessitate the state. There is no "free rider" in PD, it has nothing to do with shared resources (health care or whatever he was talking about). I think he was butchering the "problem of the common" and calling it PD.
Okay, so now I did to you guys what I wanted to do to the video guy. I don't feel any better.