**
Bivariate Uniqueness in the Logistic Recursive Distributional
Equation [***Technical Report # 629, Department of Statistics, UC,
Berkeley.* (November 2002)]

**Abstract :** In this work we prove the bivariate uniqueness
property of the logistic recursive distributional equation, which
arise in the study of the random assignment problem, as described by
Aldous (2001). Using this and the genral framework of Aldous and
Bandyopadhyay (2005), we then conclude that the associated recursive
tree process is endogenous. Thus the logistic variables defined by
Aldous (2001) for finding the limiting constant for the optimal cost
in random assignment problem turns out to be measurable with respect
the edge weights. This then answers the question raised by Aldous
(2001). The method involves construction of an explicit recursion to
show that the associated integral equation has unique solution.