This paper considers a general class of discounted Markov stochastic games characterized by multidimensional state and action spaces with an order structure, and one-period rewards and state transitions satisfying some complementarity and monotonicity conditions. Existence of pure-strategy Markov (Markov-stationary) equilibria for the …nite (in…nite) horizon game, with nondecreasing –and possib...

We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function...

In the (classical) Secretary Problem, one has to hire the best among n candidates. The candidates are interviewed, one at a time, at a uniformly random order, and one has to decide on the spot, whether to hire a candidate or continue interviewing. It is well known that the best candidate can be hired with a probability of 1/e (Dynkin, 1963). Recent works extend this problem to settings in which...

This paper addresses the issue of endogenizing the equilibrium solution when a private –domestic or foreign –…rm competes in the quantities with a public, welfare maximizing …rm. Theoretical literature on mixed oligopolies provides results and policy implications that crucially rely on the notion of equilibrium assumed, either sequential or simultaneous. In the framework of the endogenous timin...

The minimum number of edges of an undirected graph covering a symmetric , supermodular set-function is determined. As a special case, we derive an extension of a theorem of J. Bang-Jensen and B. Jackson on hypergraph connectivity augmentation. 0. INTRODUCTION T. Watanabe and A. Nakamura 1987] proved a min-max formula for the minimum number of new edges whose addition to a given undirected graph...

This article considers the problem of selecting sensors in a large-scale system to minimize error estimating its states, more specifically, state estimation mean-square (MSE) and worst-case for Kalman filtering smoothing. Such selection problems are general NP-hard, i.e., their solution can only be approximated practice even moderately large problems. Due low complexity iterative nature, greedy...

This paper is motivated by a large variety of convex or non convex problems arising in symmetric and asymmetric information models. An existence theorem is proven, based on a supermodular version of Hardy-Littlewood’s rearrangement inequalities. Sufficient conditions for monotonicity of optimal solutions are provided. Several applications to insurance are given.

We consider the scheduling problem of minimizing a weighted sum of completion times under release dates. We present a relaxation which is a supermodular polyhedron. We show that this relaxation is precisely the projection of a time-indexed relaxation introduced by Dyer and Wolsey.