electroswing

I, along with many commenters, found the explanation in Hell is Game Theory Folk Theorems somewhat unclear. I am re-explaining some of the ideas from that post here. Thanks to jessicata for writing a post on such an interesting topic. 1-shot prisoner’s dilemma. In a 1-shot prisoner’s dilemma, defecting is a dominant strategy. Because of this, (defect, defect) is the unique Nash equilibrium of this game. Which kind of sucks, since (cooperate, cooperate) would be better for both players. Nash equilibrium. Nash equilibrium is just a mathematical formalism. Consider a strategy profile, which is a list of which strategy each player chooses. A strategy profile is a Nash equilibrium if no player is strictly better off switching their strategy, assuming everyone else continues to play their strategy listed in the strategy profile. Notably, Nash equilibrium says nothing about: * What if two or more people team up and deviate from the Nash equilibrium strategy profile? * What if people aren’t behaving fully rationally? (see bounded rationality) Nash equilibria may or may not have predictive power. It depends on the game. Much work in game theory involves refining equilibrium concepts to have more predictive power in different situations (e.g. subgame perfect equilibrium to handle credible threats, trembling hand equilibrium to handle human error). n-shot prisoner’s dilemma. OK, now what if people agree to repeat a prisoner’s dilemma n=10 times? Maybe the repeated rounds can build trust among players, causing cooperation to happen? Unfortunately, the theory says that (defect, defect) is still the unique Nash equilibrium. Why? Because in the 10th game, players don’t care about their reputation anymore. They just want to maximize payoff, so they may as well defect. So, it is common knowledge that each player will defect in the 10th game. Now moving to the 9th game, players know their reputation doesn’t matter in this game, because everyone is going to defec