Fabio Lopes Stockholms universitet: Stable Bigamies on the line
This is joint work with M. Deijfen, SU
Last year Professor Lloyd Shapley was awarded the Nobel prize in economics
for his contributions to the theory of stable allocations, that is, how to
allocate as efficiently as possible agents and resources.
In this talk we construct spatial random graphs that are stable in the
sense of the Gale-Shapley stable marriage. Suppose our nodes are agents
distributed in space and their matching preferences are defined by their
distances.
Many different questions can be asked, for example, what are the typical
distances between matched agents? How are the components of such graphs?
Are there infinite components?
In the talk we focus on the last questions for a very simple setting. Our
agents are points of Poisson point processes in \mathbb{R} and each point
desires two partners (bigamy).
Deijfen, Holroyd and Peres have conjectured that in this setting with only
one type of agents, say men, there is a.s. an infinite component, while we
have shown that if there are two types of agents, say men and women, then
there is a.s. no infinite component. In the talk we explain such
difference.
Tillbaka till huvudsidan.