Seminar Announcement Date: Thursday, 5 September 2024 Time: 2:00 PM Venue: Seminar Hall Prisoner's dilemma and Cooperation Rajeeva Karandikar Chennai Mathematical Institute. 050924 Abstract Suppose two players repeatedly play Prisoner's Dilemma, without knowing that they are playing a game. We will show that if they play rationally, they end up cooperating. This uses the following result on Markov chains: Consider a Markov chain transition probability matrix P for which the eigenvalue 1 has multiplicity larger than 1 and for \epsilon>0, let P^\epsilon=(1\epsilon)P+\epsilon Q where Q is a Markov chain transition probability matrix for which eigenvalue 1 has multiplicity 1. Let \pi^\epsilon be the unique stationary distribution for P^\epsilon. We will discuss behaviour of \pi^\epsilon as \epsilon approaches 0. The talk will include required background on Markov chains. This talk is about work done over 25 years ago, appeared in Evolving Aspiration and Cooperation, Journal of Economic Theory, 1998. At the end of the talk, I will mention an open problem.
