IPDG

In a standard "prisoner's dilemma" game, the payoff matrix is set up to make Defection the dominant strategy. The concept captures a lot of situations where you could choose to do something helpful to others (= Cooperate, in the IPDG) and if everybody cooperates, everybody wins. But in many of these situations, if everybody else is cooperating, you can personally maximize by Defecting. You gain the benefits of everybody else cooperating, but you don't bear the cost of cooperating.

Example: picking up litter. If everybody does it, the environment gets clean. But if everybody else is doing it, you can stop doing it and get the benefit of the clean environment (somebody else will pick it up) without doing the work. But, if everybody starts to Defect and you still Cooperate, now you get all the cost and no real benefit.

An interesting payoff matrix looks something like:
Coop/Coop: +1/+1
Defect/Coop: +2/-5 (and vice versa)
Defect/Defect: -1/-1

In these kinds of games, the math is pretty clear that absent external knowledge of what the other actor will do, you are best served to Defect. In iterated games where you have some knowledge over time of what the other actor does, the tit-for-tat strategy is optimal (do to the other person whatever they did to you last, but cooperate on the first trial).

The math implies a puzzle about why people engage in altruism -- why cooperate at all? Are people not rational? Or do they expect some return from their reputation -- if you cooperate and re-engage the same person later and they remember you, perhaps they'll cooperate back and you'll get a return on your invested cost. The math seems to depend on the probability of reciprocation.

Douglas Hofstadter, however, points out another reason to cooperate which he calls Superrationality. The idea is that if you know your opponent/partner is extremely insightful, you might both be able to reason in a way that leads to similar conclusions. E.g., you both realize the game is Defect dominant, so you'll both initially think to defect. But you both also realize that given that you will both choose the same option, you could safely cooperate knowing the other person will also find the reason to cooperate and you'll get to the C-C outcome.

Whether people actually think that way is one thing, but it does point out the value of symmetry in the game. Any time 2 actors choose the same action, the result is "fair" to both of them and optimal for them combined if they both cooperate. The payoff matrix described above is also designed to maximize the joint outcome in the C-C cell.

If we extend the IPDG beyond two-person interactions to think of the welfare of a collection of individuals (who each interact in pairs), it's clear that maximizing the community welfare is done by maximizing the number of C-C interactions. This is a situation where you personally maximize your utility by Defecting, but your community is maximized by Cooperating.

If we imagine a large number of competing communities out in the world, what is the optimal way for a community to out-compete other communities?

Two things that will help a lot are: (1) social norms defined in the community that encourage/require cooperation as much as possible and (2) in-group/out-group biases.

On (1), communities with strong social norms that require people to set aside personal gain and cooperate for communal benefit will out-compete more individualistic communities. In fact, for the specific payoff matrix above, you don't strictly need a cooperation/altruism directive, you can actually get the communal benefit mainly through symmetry. If you have a very homogeneous set of actors (who all think alike), they should tend to come to cooperate/defect decisions the same way and tend to end up in the C-C or D-D cells (which are community maximizing). Also, if there's any learning in the actors, experience with only C-C or D-D interactions will tend to reinforce Cooperating over Defection and the community will move towards general altruism.

On (2), it's obvious that if you want your community to out-compete other communities, you want to maximize Cooperation (altruism) within your community, but personally maximize utility outside and Defect (or at best tit-for-tat).

Curiously, this seems to imply that if you have many communities competing over a long period of time and success is related to how well your community structure maximizes outcomes, communities that construct very strong social norms, homogeneous thinking and strong out-group biases should tend to win. Does this provide insight into the prevalance of groups that organize around religions that are particularly controlling, nationalism (and strong cultural expectations) and even racism?