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        riddles >> easy >> Infinite games
        
(Message started by: mistaken_id on Mar 12^th, 2009, 5:00pm)

Title: Infinite games
Post by mistaken_id on Mar 12^th, 2009, 5:00pm

Why is Co-operation a nash equilibrium when two players play prisoners dilemma infinitely many times?

If any one of you dont know what a prisoners dilemma is

http://en.wikipedia.org/wiki/Prisoner%27s_dilemma

Title: Re: Infinite games
Post by towr on Mar 13^th, 2009, 2:12am

Both players adopting the strategy of always cooperating isn't a Nash equilibrium. Because either is better off defecting as long as the other keeps cooperating.
Both players adopting the tit-for-tat strategy is a Nash equilibrium, because neither player is, over the course of an infinite number of games, better off unilaterally switching to another strategy. And while they do end up always cooperating, it isn't quite the same thing.