Sorting out single-crossing preferences on networks

<Para ID="Par1">We extend the single-crossing property to tree networks to facilitate its application in network games. It is equivalent to intermediate preferences and order restriction (also extended to networks). Moreover, to facilitate broader applications in real world cases and simulations, we develop algorithms that answer the following two questions. Given a preference profile, can we construct a tree graph that supports single-crossing? Given a set of alternatives, can we generate single-crossing preference profiles with associated tree graphs? Copyright Springer-Verlag Berlin Heidelberg 2015