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作者：Dunkel, Juliane; Schulz, Andreas S.
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The question as to whether the Gomory-Chvatal closure of a nonrational polytope is a polytope has been a longstanding open problem in integer programming. In this paper, we answer this question in the affirmative by combining ideas from polyhedral theory and the geometry of numbers.
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作者：Jaskiewicz, Anna; Matkowski, J.; Nowak, A. S.
作者单位：Wroclaw University of Science & Technology; University of Zielona Gora
摘要：In this paper we study a Markov decision process with a nonlinear discount function. First, we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values. It turns out that the associated optimization problem leads to a nonstationary dynamic programming and an infinite system of Bellman equations, which result in obtaining persistently optimal policies. Our theory is enriched by examples.
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作者：Wiesemann, Wolfram; Kuhn, Daniel; Rustem, Berc
作者单位：Imperial College London
摘要：Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use because of their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider robust MDPs that offer probabilistic guarantees in view of the unknown parameters. To this end, we assume that an observa...
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作者：Drapeau, Samuel; Kupper, Michael
作者单位：Humboldt University of Berlin
摘要：To address the plurality of interpretations of the subjective notion of risk, we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity. Our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets. This representation covers most instruments related to risk and allows for a differentiated interpretation depending on the underlying context that is illus...
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作者：Cohen, Asaf; Solan, Eilon
作者单位：Tel Aviv University
摘要：Bandit problems model the trade-off between exploration and exploitation in various decision problems. We study two-armed bandit problems in continuous time, where the risky arm can have two types: High or Low; both types yield stochastic payoffs generated by a Levy process. We show that the optimal strategy is a cut-off strategy and we provide an explicit expression for the cut-off and for the optimal payoff.
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作者：Acemoglu, Daron; Como, Giacomo; Fagnani, Fabio; Ozdaglar, Asuman
作者单位：Massachusetts Institute of Technology (MIT); Lund University; Polytechnic University of Turin; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents: (1) regular agents who update their beliefs according to information that they receive from their social neighbors and (2) stubborn agents who never update their opinions and might represent leaders, political parties, or media sources at...
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作者：von Falkenhausen, Philipp; Harks, Tobias
作者单位：Technical University of Berlin; Maastricht University
摘要：Joint use of resources with usage-dependent cost raises the question: who pays how much? We study cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources. Our goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability. We investigate three classes of protocols: basic protocols guarantee the existence of at least one pure Nash equilibrium; separable...
