Abstract
We consider a discrete time Markov chain whose state space is the set of all N× N stochastic matrices with zero diagonal entries. This chain models the evolution of relationships among N individuals who exchange gifts according to probabilities determined by previous exchanges. We determine the stable equilibria for this chain, and prove convergence to a mixture of these. In particular, we show that for generic initial states, the chain converges to a randomly chosen set of constellations made up of disjoint stars. Each star has a center, which is the recipient of all gifts from the other individuals in that star, while the center distributes his gifts only to members of his own star.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
