Colloquium Mathematics - Prof. Maria Deijfen University of Stockholm

Title: Friendly frogs, stable matchings and the magic of invariance

Abstract:

Consider the following two-player game. A set of points in R^d
is fixed - we can imagine (for the two-dimensional case) that these are
locations of lilypads on a pond. There are two frogs and two players
take turns to move a frog to an unoccupied lilypad in such a way that
the distance between the frogs is strictly decreased. A player that
cannot move loses. We analyze this game and some variants of it,
discovering links to a range of models of stable matchings. We focus
particularly on the case of random infinite sets, where we use
invariance, ergodicity, mass transport and deletion-tolerance to
determine game outcomes.