The Prisoner’s Dilemma is a simple game designed to show how the success or failure of cooperation between individuals can be contingent on various factors, primarily some sort of reward. Shown above is a representative payoff matrix between two players; each square shows the two choices and the two winnings for each. Each player cooperates (A or B) or cheats (A’ or B’) with the other player, so for example if A and B’ obtains (A cooperates but B cheats) then A loses 1 and B wins 3.
Each player knows all the values of the payoff matrix so it is said they have perfect information, except they don’t know what their opponent will do. If they are rational and believe their opponent to be as well, the wisest thing to do is for both to cooperate to maximize their winnings, knowing that their opponent knows that they could also cheat. If the game is played only once, however, that is clearly not the case.
If the game is iterated, things change. If each player remembers what their opponent did previously, and it is considered to be informative for what they might do next, then the player could use it to condition their decision to cooperate or cheat. Different algorithms or personalities can be considered for the players, with more or less thinking about what to do and more or less willingness to cooperate, and it is interesting to try different strategies, all the while seeing what adjustments of the payoff matrix might do to the results.
This Evolution of Trust site is a very nice lesson in some of the complications that can result for such algorithms and adjustments. On the whole, this site indicates that rationality and consideration for others can thrive, if conditions are right. In the traditional Prisoner’s Dilemma, the reward values in the payoff matrix are usually considered to be jail sentence time (so less is better), or for the site mentioned above where I’ve taken the representative matrix, monetary value (so more is better).
One thing of note in these examples is that each player doesn’t distinguish their opponent by anything other than their posteriori plays, because these players are supposed to be all part of the same group or society. But what if there is an a priori distinction that conditions their decision? So, if your opponent is a known Y, and you are a X, then you might want to raise your social credit with your other Xs by punishing a Y, even if it punishes you or even other Xs in the long run.
For example if you are a member of gang X, you wouldn’t want to cheat against another X. But cheating against a member of gang Y might raise your in-group social capital and be as important as the value of the reward. Or you might want to punish your opponent in group Y by not granting them any benefits even at the cost of your own benefit. Such distinctions are not usually part and parcel of the Prisoner’s Dilemma game, but they would add an interesting and realistic dimension to the game.
And thus lend insight into the woes of our modern political scene and culturally diverse society.