# Bivariate Uniqueness in the Logistic Recursive Distributional Equation

Report Number
629
Authors
In this work we prove the \emph{bivariate uniqueness} property of the Logistic fixed-point equation, which arise in the study of the \emph{random assignment problem}, as discussed by Aldous (2001). Using this and the general framework of Aldous and Bandyopadhyay (2002), we then conclude that the associated \emph{recursive tree process} is \emph{endogenous}, and hence the Logistic variables defined in Aldous' 2001 paper are measurable with respect to the $\sigma$-field generated by the edge weights. The method involves construction of an explicit recursion to show the uniqueness of the associated integral equation.