Eigenfunctions Seminar

Slides
Title: Perron–Frobenius eigenfunctions of perturbed stochastic matrices
Speaker: Rajeeva L. Karandikar (CMI, Chennai)
Date: 27 September 2019
Time: 3 – 5 pm (with a 15 minute break at 3:45)
Venue: LH-1, Mathematics Department

Consider a stochastic matrix $P$ for which the Perron–Frobenius eigenvalue has multiplicity larger than 1, and for $\epsilon > 0$, let

where $Q$ is a stochastic matrix for which the Perron–Frobenius eigenvalue has multiplicity 1. Let $\pi^\epsilon$ be the Perron–Frobenius eigenfunction for $P^\epsilon$. We will discuss the behavior of $\pi^\epsilon$ as $\epsilon \to 0$.

This was an important ingredient in showing that if two players repeatedly play Prisoner’s Dilemma, without knowing that they are playing a game, and if they play rationally, they end up cooperating. We will discuss this as well in the second half.

The talk will include the required background on Markov chains.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 15 Nov 2019