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作者：Aspect, Leopold; Ewerhart, Christian
作者单位：University of Zurich
摘要：Sion and Wolfe [Sion M, Wolfe P (1957) On a game without a value. Contributions to the Theory of Games III, Annals of Mathematics Studies (Princeton University Press, Princeton, NJ), 299-306.] presented a two-person zero-sum game on the unit square without a value. In the present paper, we analyze finite-grid approximations of the Sion-Wolfe game. We find that, as the number of grid points tends to infinity and the payoff function approaches that of the infinite game, the limiting value of fin...
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作者：Alidou, Abdou Majeed; Hazla, Jan; Baligacs, Julia; Hahn-Klimroth, Max; Hintze, Lukas; Scheftelowitsch, Olga
作者单位：University of Oxford; Goethe University Frankfurt; University of Hamburg; Dortmund University of Technology
摘要：Polarization and unexpected correlations between opinions on diverse topics are an object of sustained attention. However, numerous theoretical models do not seem to convincingly explain these phenomena. This paper is motivated by a recent line of work, studying models where polarization can be explained in terms of biased assimilation and geometric interplay between opinions on various topics. The agent opinions are represented as unit vectors on a multidimensional sphere and updated accordin...
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作者：Huo, Dongyan (Lucy); Chen, Yudong; Xie, Qiaomin
作者单位：Hong Kong University of Science & Technology; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider linear stochastic approximation (LSA) with constant step size and Markovian data. Viewing the joint process of the data and LSA iterate as a time-homogeneous Markov chain, we prove its convergence to a unique limiting and stationary distribution and establish nonasymptotic, geometric convergence rates. Furthermore, we show that the bias vector of this limit admits an infinite series expansion with respect to the step size. Consequently, the bias is proportional to the step size up ...
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作者：Wang, Yike; Liu, Jingzhen; Yiu, Ka-Fai Cedric; Siu, Tak Kuen
作者单位：Chongqing Technology & Business University; Central University of Finance & Economics; Hong Kong Polytechnic University; Macquarie University
摘要：This paper studies consumption-portfolio optimization problems with habit formation in a regime-switching market. The habit level, which reflects the endogenous impact of past consumption, also involves regime switching and jump diffusion. Because of the presence of general utility functions and path-dependent random parameters, we use the market completion method and introduce some additional jump assets to address the problems. After reducing the problems to solving a stochastic Hamilton-Jac...
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作者：Chorobura, Flavia; Necoara, Ion; Pesquet, lean-Christophe
作者单位：National University of Science & Technology POLITEHNICA Bucharest; Romanian Academy; Universite Paris Saclay; Inria
摘要：In this paper, we propose an adaptive forward-backward-forward splitting algorithm for finding a zero of a pseudo-monotone operator that is split as a sum of three operators: the first is continuous single-valued, the second is Lipschitzian, and the third is maximally monotone. This setting covers, in particular, constrained minimization scenarios, such as problems having smooth and convex functional constraints (e.g., quadratically constrained quadratic programs) or problems with a pseudo-con...
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作者：Cembrano, Javier; Correa, Jose; Schmidt-Kraepelin, Ulrike; Tsigonias-Dimitriadis, Alexandros; Verdugo, Victor
作者单位：Max Planck Society; Universidad de Chile; Eindhoven University of Technology; European Central Bank; Pontificia Universidad Catolica de Chile; Pontificia Universidad Catolica de Chile
摘要：The apportionment problem constitutes a fundamental problem in democratic societies: How to distribute a fixed number of seats among a set of states in proportion to the states' populations? This-seemingly simple-task has led to a rich literature and has become well known in the context of the U.S. House of Representatives. In this paper, we connect the design of monotone apportionment methods to classic problems from discrete geometry and combinatorial optimization and explore the extent to w...
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作者：Chen, Lin; Tao, Liangde; Verschae, Jose
作者单位：Zhejiang University; Pontificia Universidad Catolica de Chile; Pontificia Universidad Catolica de Chile
摘要：We consider a classical scheduling problem on m identical machines. For an arbitrary constant q > 1, the aim is to assign jobs to machines such that Sigma(m)(i=1) C-i(q) is minimized, where C-i is the total processing time of jobs assigned to machine i. It is well known that this problem is strongly NP-hard. Under mild assumptions, the running time of a (1 + epsilon)-approximation algorithm for a strongly NP-hard problem cannot be polynomial on 1/epsilon, unless P=NP. For most problems in the ...
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作者：Lassiter, Julie Bowers; Hadavas, Paul T.; Adams, Warren P.
作者单位：Clemson University; University System of Georgia; Georgia Southern University
摘要：We define a multilinear program to be persistent if every variable realizing a value at either its lower or upper bound in an optimum to a specified linear relaxation persists in retaining that same value in an optimum to the original problem. Few persistency results are known, and all deal with binary or mixed 0-1 problems, reformulating nonlinear instances as equivalent mixed 0-1 linear programs and showing the preference of a binary variable over its complement. We extend the knowledge of p...
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作者：Kruk, Lukasz
作者单位：Maria Curie-Sklodowska University
摘要：A single-server queue with renewal arrivals and generally distributed independent and identically distributed service times is considered. Customers are served using the longest job first (LJF) scheduling algorithm with first in, first out being used as a tiebreaking rule. We introduce a fluid model for the evolution of a measure-valued state descriptor of this queue, and we investigate its properties. We also prove a fluid limit theorem justifying our fluid model as the first order approximat...
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作者：Aydin, Ugur; Saldi, Naci
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Ihsan Dogramaci Bilkent University
摘要：In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish convergence conditions for value iterationbased algorithms in mean-field games. Subsequently, utilizing these results, we demonstrate that the mean-field equilibrium obtained through this value iteration algorithm remains robust even in the face of system dynamics mis...
