First, we discovered in the experiment that PD actually has 3 actions. Cooperate, defect, and ... wait as long as possible to defect to punish your opponent who is not cooperating. This happened because participants are playing in a real-time web app, and they have some time to make a decision. Although there is a lot of literature on how costly punishment can be used to enforce cooperation, it was pretty amazing how it emerged organically in our study after a few days. Someone could certainly grab our dataset and get a free publication out of just that.
Also, given the month-long design of the study, we were thinking of something where players get to stay on or "die" based on their daily score, and therefore the population evolves based on who gets the highest payoffs. Evolutionary game theory has some ideas about this, but they are all theoretical or simulation, and not conducted with real people. I'm actually not sure if cooperation would be sustained or not in this design, but I agree that it would go a long way toward pinning down the origins of cooperation. I also agree with you that groups or network structure would affect the result a lot, allowing cooperative bands to flourish even when defectors are running around.
To add the option to "wait/defer", you could include informational incentives/variance where players gain the ability to increase their perspective and degrees of freedom by being privy to more information sooner. For example, once a player achieves some level of points/reputation, they gain the ability to see the other player's move before they move -- this would in effect be giving them the power to defer. The other player may or may not know the extent of the other player's abilities at that time -- one or both may have the ability to see (defer), and neither may know for sure. For example, rather than explicitly stating upfront to new players that through their play they can improve their ability to see, let players discover this once they cross a threshold. Further increased powers might include the ability to see into the other player's past games, see their group's dynamics or portions of the wider network, and communicate with other group members and/or the other player during games.
As stated by Axelrod in EoC, one feature of the tit-for-tat strategy is that it's easy enough that it can be understood by anyone, and it's simple enough that it can be communicated/signaled from one player to the other through their play. It would be interesting to see how learned players -- who have gained the ability to see -- use or abuse their elevated powers of sight, either by working to better signal/communicate their intent and teach the winning strategy to the less enlightened players or by choosing to try and exploit the naivety of the other player who may be relatively blind.
https://en.wikipedia.org/wiki/Jonathan_Haidt
NB: Also see this timely post on "information theory and the foundations of life" https://news.ycombinator.com/item?id=13496133
http://www.ted.com/talks/jonathan_haidt_humanity_s_stairway_...
Also this Edge article on "Contingent Superorganism" https://www.edge.org/response-detail/10386
The 3rd option used most widely in business today. Defectors are "punished" by refusing to do business with them after a defection.
Give players the ability to remember players they have engaged with and add a third option: 1. Cooperate 2. Defect 3. Wait (defer, don't engage, don't play). New players will seek out players and offer to engage with them. When you defect, your reputation history declines, and when you die, your reputation history resets to zero and you lose the option to defer.
HYPOTHESIS: Cooperators will wait/defer, Defectors will wait/defer, new players will choose to cooperate or defect, and since defecting against defer is an all-but-certain lose, new players will choose to cooperate hoping the other player will too. Cooperators will naturally organize into groups of cooperators and flourish. Players in cooperator groups will cooperate tit-for-tat with known cooperators and will wait/defer with known defectors or new/unknown players no one in the cooperator group has engaged with (call it the no-fools strategy). New players and players who have been struggling in the wilderness outside of cooperative groups will want to get into a cooperative group and so they will seek to engage with players using the tit-for-tat strategy until they find a cooperative group (call it the pay-it-forward strategy). Fools who don't learn will stumble around in the wilderness until they eventually die off.