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作者：Jasin, Stefanus; Kumar, Sunil
作者单位：University of Michigan System; University of Michigan; University of Chicago
摘要：We consider a network revenue management problem with customer choice and exogenous prices. We study the performance of a class of certainty-equivalent heuristic control policies. These heuristics periodically re-solve the deterministic linear program (DLP) that results when all future random variables are replaced by their average values and implement the solutions in a probabilistic manner. We provide an upper bound for the expected revenue loss under such policies when compared to the optim...
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作者：Xu, Huan; Mannor, Shie
作者单位：National University of Singapore; Technion Israel Institute of Technology
摘要：We consider Markov decision processes where the values of the parameters are uncertain. This uncertainty is described by a sequence of nested sets (that is, each set contains the previous one), each of which corresponds to a probabilistic guarantee for a different confidence level. Consequently, a set of admissible probability distributions of the unknown parameters is specified. This formulation models the case where the decision maker is aware of and wants to exploit some (yet imprecise) a p...
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作者：Fibich, Gadi; Gavish, Nir
作者单位：Tel Aviv University
摘要：We introduce a new approach for analysis and numerical simulations of asymmetric first-price auctions, which is based on dynamical systems. We apply this approach to asymmetric auctions in which players' valuations are power-law distributed. We utilize a dynamical-systems formulation to provide a proof of the existence and uniqueness of the equilibrium strategies in the cases of two coalitions and of two types of players. In the case of n different players, the singular point of the original s...
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作者：Del Pia, Alberto
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Let L be a family of lattice-free polyhedra in R-m containing the splits. Given a polyhedron P in Rm+n, we characterize when a valid inequality for P boolean AND (Z(n) x R-n) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L for every polyhedron P. Our resu...
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作者：Busic, Ana; Vliegen, Ingrid; Scheller-Wolf, Alan
作者单位：Inria; Universite PSL; Ecole Normale Superieure (ENS); University of Twente; Carnegie Mellon University
摘要：Solving Markov chains is, in general, difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs bounds by redirecting selected sets of transitions, facilitating an intuitive interpretation of th...
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作者：Kella, Offer; Ramasubramanian, S.
作者单位：Hebrew University of Jerusalem; Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：A reflection map, induced by the deterministic Skorohod problem on the nonnegative orthant, is applied to a vector-valued function X on the nonnegative real line and then to a + X, where a is a nonnegative constant vector. A question that was posed over 15 years ago is, under what conditions does the difference between the two resulting regulated functions converge to zero for any choice of a as time diverges. This, in turn, implies that if one imposes enough stochastic structure that ensures ...
