We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular function or minimize a nonincreasing supermodular function in the setting of bounded total curvature c. In the case of submodular maximization with curvature ...

In this paper we study the complexity of the (weighted) maximum constraint satisfaction problem (Max CSP) over an arbitrary finite domain. In this problem, one is given a collection of weighted constraints on overlapping sets of variables, and the goal is to find an assignment of values to the variables so as to maximize the total weight of satisfied constraints. Max Cut is a typical example of...

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy is presented under the assumption correlated noise in signals. A model given using truncated modes modeling, positions that are optimal generalized least squares estimation selected. The determinant covariance matrix error minimized...

In view of the problem that it is difficult to quantitatively assess interactivity between attributes in identification process 2-order additive fuzzy measure, this work uses intuitionistic sets (IFSs) describe and deal with attributes. Firstly, defined by supermodular game theory. On basis, experts employ number (IFN) attributes, Secondly, opinions all are aggregated using weighted average ope...

Recently Yang and Qi (2013) stated an interesting theorem on existence of complete lattice of equilibria in a particular class of large nonatomics supermodular games for general action and types spaces. Unfortunately, their result is incorrect. In this note, we detail the nature of the problem with the stated theorem, provide a counterexample, and then correct the result under additional assump...

This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on Aand E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum eigenvalue of the estimation error covariance matrix are not supermodular. To do so, it leverages the concept of approximate supermodularity to derive nonasymp...

We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs in Vives (1990) and Milgrom and Roberts (1990): (a) we use the interim formulation of a Bayesian game, in which each player’s beliefs are part of his or her type rather than being derived from a prior; (b) we ...

In this work we study situations in which communication among the players is not complete and it is represented by a family of subsets of the set of players. Although several models of partial cooperation have been proposed, we shall follow a model derived from the work of Faigle and Kern. We define the games on convex geometries and introduce marginal worth vectors and quasi-supermodular games...

This note demonstrates that symmetric 3× 3 supermodular games may fail to have any equilibrium robust to incomplete information. Since the global game solution in these games is known to be independent of the noise structure, our result implies that a noise-independent selection in global games may not be a robust equilibrium. Journal of Economic Literature Classification Numbers: C72, D82.

In this paper we extend the basic model of Cournot competition to the case where both the demand function and the cost functions of each firm depend on the amounts produced by competitors. In this modified setting, proving existence of equilibria becomes harder. We develop a generalization of the theory of supermodular games in the context where individual decision variables take values in a to...