Two results from Mandelbaum's paper: "The dynamic complementarity problem"

TL;DR

This paper discusses two key results from Mandelbaum's unpublished 1987 work on the dynamic complementarity problem, focusing on the uniqueness and non-uniqueness of solutions to a two-dimensional Skorokhod problem.

Contribution

It provides accessible explanations of two important results on the Skorokhod problem, including a counterexample and a proof of uniqueness in a critical case.

Findings

Example of non-uniqueness in a 2D Skorokhod problem

Proof of uniqueness in a critical case of the 2D Skorokhod problem

Clarification of Mandelbaum's results not readily available in literature

Abstract

A draft of a paper by Mandelbaum, "The dynamic complementarity problem", was circulated in 1987, but has never been published. We give an exposition of two important results from that paper which are not readily accessible in the literature. The first is an example of a Skorokhod problem in two dimensions in the quadrant for which there is not uniqueness. The second is a proof of uniqueness for the Skorokhod problem in two dimensions in the quadrant in a critical case.