Game Theory of the Immortals

by Crystalist1 min read11th Mar 201314 comments


Personal Blog

I’m sure many others have put much more thought into this sort of thing -- at the moment, I’m too lazy to look for it, but if anyone has a link, I’d love to check it out.

Anyway, I ran into some interesting musings on game theory for immortal agents and I thought it was interesting enough to talk about.

Cooperation in games like the iterated Prisoner’s Dilemma is partly dependent on the probability of encountering the other player again. Axelrod (1981) gives the payoff for a sequence of 'cooperate's as R/(1-p) where R is the payoff for cooperating, and p is a discount parameter that he takes as the probability of the players meeting again (and recognizing each other, etc.). If you assume that both players continue playing for eternity in a randomly mixing, finite group of other players, then the probability of encountering the other player again approaches 1, and the payoff for an extended period of cooperation approaches infinity.

So, take a group of rational, immortal agents, in a prisoner’s dilemma game. Should we expect them to cooperate?

I realize there is no optimal strategy without reference to the other players’ strategies, and that the universe is not actually infinite in time, so this is not a perfect model on at least two counts, but I wanted to look at the simple case before adding complexities.