The paper provides a possible explanation for the occurrence of uniform, fixedproportion rules for sharing surplus in two-sided markets. We study a two-sided matching model with transferable utility where agents are characterized by privately known, multi-dimensional attributes that jointly determine the surplus of each potential partnership. We ask the following question: for what divisions of...

We consider the problem of finding a uniform hypergraph that satisfies cut demands defined by a symmetric crossing supermodular set function. We give min-max formulas for both the degree specified and the minimum cardinality problem. These results include as a special case a formula on the minimum number of r-hyperedges whose addition to an initial hypergraph will make it k-edge-connected.

We show that the decoding problem in generalized Higher Order Conditional Random Fields (CRFs) can be decomposed into two parts: one is a tree labeling problem that can be solved in linear time using dynamic programming; the other is a supermodular quadratic pseudo-Boolean maximization problem, which can be solved in cubic time using a minimum cut algorithm. We use dual decomposition to force t...

Let N be a ...nite set. By a closure space we mean the family of the closed sets of a closure operator on 2 satisfying the additional condition ; = ;. A simple game on a closure space L is a function v : L ! f0; 1g such that v(;) = 0 and v (N) = 1. We assume simple games are monotonic. The coalitions are the closed sets of L and the players are the elements i 2 N . We will give results concerni...

We revisit the analysis of discrete comparative statics effects in the classical consumer expenditure minimization framework, using techniques that exploit the order and lattice properties of the problem, without reference to topological properties. It is shown that these comparative statics effects give rise to classes of partial orders, which in turn induce lattice structures that define the ...

We consider partial bandwagon properties in the context of coordination games to capture the idea of weak network externalities. We then study a local interactions model where agents play a coordination game following a noisy best-reply process. We identify conditions such that Globally Pairwise Risk Dominant strategies are selected. Examples include arbitrary 3× 3 coordination games and n×n su...

Behind a stable and relatively high fertility level in Norway during the 1990s we find increasing differences in the pattern of fertility both in regard to the timing of the first childbirth and number of children born. In this paper, data from the Central Population Register in Norway are used to provide a review of recent fertility trends and discuss the consequences of education level on dif...

This paper is dedicated to the risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the convex ordering of their corresponding m...

We introduce a class of discrete point processes that we call the Submodular Point Processes (SPPs). These processes are characterized via a submodular (or supermodular) function, and naturally model notions of information, coverage and diversity, as well as cooperation. Unlike Log-submodular and Log-supermodular distributions (Log-SPPs) such as determinantal point processes (DPPs), SPPs are th...

Submodular and supermodular functions have found wide applicability in machine learning, capturing notions such as diversity and regularity, respectively. These notions have deep consequences for optimization, and the problem of (approximately) optimizing submodular functions has received much attention. However, beyond optimization, these notions allow specifying expressive probabilistic model...