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作者：Guo, Xianping
作者单位：Sun Yat Sen University
摘要：This paper deals with continuous-time Markov decision processes in Polish spaces, under an expected discounted reward criterion. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We first give conditions on the controlled system's primitive data. Under these conditions we prove that the transition functions of possibly nonhomogeneous continuous-time Markov processes are regular by ...
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作者：Carassus, Laurence; Rasonyi, Miklos
作者单位：Universite Paris Cite; Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control
摘要：A discrete-time financial market model is considered with a sequence of investors whose preferences are described by their utility functions U-n, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever U-n tends to another utility function U-infinity the respective optimal strategies converge, too. Under additional assumptions the rate of convergence is estimated. We also establish the continuity of the fair price o...
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作者：Cheevaprawatdomrong, Torpong; Schochetman, Irwin E.; Smith, Robert L.; Garcia, Alfredo
作者单位：Oakland University; University of Michigan System; University of Michigan; University of Virginia
摘要：We consider a nonhomogeneous infinite-horizon Markov Decision Process (MDP) problem with multiple optimal first-period policies. We seek an algorithm that, given finite data, delivers an optimal first-period policy. Such an algorithm can thus recursively generate, within a rolling-horizon procedure, an infinite-horizon optimal solution to the original problem. However, it can happen that no such algorithm exists, i.e., the MDP is not well posed. Equivalently, it is impossible to solve the prob...
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作者：Naddef, Denis; Rinaldi, Giovanni
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Consiglio Nazionale delle Ricerche (CNR); Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti (IASI-CNR)
摘要：The path, the wheelbarrow, and the bicycle inequalities have been shown by Cornuejols, Fonlupt, and Naddef to be facet-defining for the graphical relaxation of STSP(n), the polytope of the symmetric traveling salesman problem on an n-node complete graph. We show that these inequalities, and some generalizations of them, define facets also for STSP(n). In conclusion, we characterize a large family of facet-defining inequalities for STSP(n) that include, as special cases, most of the inequalitie...
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作者：Jofre, Alejandro; Rockafellar, R. Terry; Wets, Roger J-B.
作者单位：Universidad de Chile; Universidad de Chile; University of Washington; University of Washington Seattle; University of California System; University of California Davis
摘要：Variational inequality representations are set up for a general Walrasian model of consumption and production with trading in a market. The variational inequalities are of functional rather than geometric type and therefore are able to accommodate a wider range of utility functions than has been covered satisfactorily in the past. They incorporate Lagrange multipliers for budget constraints, which are shown to lead to an enhanced equilibrium framework with features of collective optimization. ...
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作者：Leizarowitz, Arie; Zaslavski, Alexander J.
作者单位：Technion Israel Institute of Technology
摘要：In this paper we consider infinite horizon discrete-time optimal control of Markov decision processes (MDPs) with finite state spaces and compact action sets. We restrict attention to unicost MDPs, which form a class that contains all the weakly communicating MDPs. The unicost MDPs are characterized as those MDPs for which there exists a solution to the single optimality equation. We address the problem of uniqueness and stability of minimizing Markov actions. Our main result asserts that when...
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作者：Simsek, Alp; Ozdaglar, Asuman; Acemoglu, Daron
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：This paper presents an extension of the Poincare-Hopf theorem to generalized critical points of a function on a compact region with nonsmooth boundary, M, defined by a finite number of smooth inequality constraints. Given a function F: M -> R, we define the generalized critical points of F over M, define the index for the critical point, and show that the sum of the indices of the critical points is equal to the Euler characteristic of M. We use the generalized Poincare-Hopf theorem to present...
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作者：Richman, Oran; Shimkin, Nahum
作者单位：Technion Israel Institute of Technology
摘要：We consider the problem of selfish routing in a congested network shared by several users, where each user wishes to minimize the cost of its own flow. Users are atomic, in the sense that each has a nonnegligible amount of flow demand, and flows may be split over different routes. The total cost for each user is the sum of its link costs, which, in turn, may depend on the user's own flow as well as the total flow on that link. Our main interest here is network topologies that ensure uniqueness...
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作者：Acemoglu, Daron; Ozdaglar, Asuman
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We study the efficiency of oligopoly equilibria (OE) in congested markets. The motivating examples are the allocation of network flows in a communication network or of traffic in a transportation network. We show that increasing competition among oligopolists can reduce efficiency, measured as the difference between users' willingness to pay and delay costs. We characterize a tight bound of 5/6 on efficiency in pure strategy equilibria when there is zero latency at zero flow and a tight bound ...
