The benefits of cooperation can't be modeled so simplistically, since the concepts of both long-term reputation and long-term retribution need to be taken into account.
You don't need any model to explain inconsistency. People are not consistent because they are learning the rules and results of the game as they play. The players' first move might be somewhat random, but every subsequent move is based upon their previous experiences with the game. That is why you do these things iteratively.
Sometimes I wish life was just like that Black Mirror episode with reputation scores for everybody. Nobody wants to cooperate because there is hardly any long term reputation to worry about when interacting with most people (ie cutting off that car in the highway, being rude to that stranger next to you)
The point here was that credit scores do not only rate your own behavior, but also those of people around you. If your neighborhood is bad, your credit score might reflect that instead of your own performance as a debtor. And if your neighborhood becomes hip and gains a better reputation, your credit score might improve even though you're still the same person.
Capitalism sometimes rewards those who provide value, but more often than not has no problem rewarding people for spouting self-righteousness.
If you think that everyone who gets rewarded in a capitalist society do so because they provide value then you have to ask: What value do scam artists provide?
Society, and even biology, has invented all sorts of mechanism to reward/punish you for actions. The emotion of shame, for example, is a strong incentive to behave as expected, even among strangers. Shame (and pride) are probably evolutionary adaptions to make the connection between an action and the resulting change in your reputation more immediate.
On the other end of the scale, criminal law punishes you for large transgressions, and sometimes prizes reward you for good deeds (although the latter is mostly achieved via market mechanisms).
Both criminal law and awards also work via reputation, by publicising your actions to a wide audience.
It's also interesting to contrast the discussion in this threat to any number of HN threats on freedom of speech in the last weeks. There, the idea that someone's reputation could be tarnished by their participation in a neo-nazi torch parade was generally considered to be the end of freedom.