Turnpike Theorems for Markov Games

Kolokoltsov, Vassili N.; Yang, Wei

doi:10.1007/s13235-012-0047-6

Cited by 49 publications

(21 citation statements)

References 92 publications

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“…In Section 4 we obtain our main result; we construct the class of time-dependent solutions that stay in a neighbourhood of the identified stationary solution. In the terminology of mathematical economics, this stationary solution represents a turnpike (see, e.g., Kolokoltsov and Yang (2012); Zaslavski (2006)) for the class of time-dependent solutions.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary, mean-field and pressure-resistance game modelling of networks security

Katsikas¹,

Kolokoltsov²

2019

Journal of Dynamics &Amp; Games

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The recently developed mean-field game models of corruption and bot-net defence in cyber-security, the evolutionary game approach to inspection and corruption, and the pressure-resistance game element, can be combined under an extended model of interaction of large number of indistinguishable small players against a major player, with focus on the study of security and crime prevention. In this paper we introduce such a general framework for complex interaction in network structures of many players, that incorporates individual decision making inside the environment (the mean-field game component), binary interaction (the evolutionary game component), and the interference of a principal player (the pressure-resistance game component).To perform concrete calculations with this overall complicated model, we suggest working, in sequence, in three basic asymptotic regimes; fast execution of personal decisions, small rates of binary interactions, and small payoff discounting in time.

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Section: Introductionmentioning

confidence: 99%

Evolutionary, mean-field and pressure-resistance game modelling of networks security

Katsikas¹,

Kolokoltsov²

2019

Journal of Dynamics &Amp; Games

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“…See, for example, [2-4, 6-11, 13, 14, 16, 19, 20, 22, 25, 27, 32-34, 36, 37, 46-49, 51, 52] and the references mentioned therein. These problems arise in engineering [1,23,44,56,57], in models of economic growth [12, 13, 17, 22, 26, 31, 35, 39-41, 44, 45, 53, 55], in the game theory [18,21,43,44,50,53,54], in infinite discrete models of solid-state physics related to dislocations in one-dimensional crystals [5,42], and in the theory of thermodynamical equilibrium for materials [15,24,[28][29][30]. In this chapter we explain the turnpike phenomenon for a simple class of variational problems, discuss certain turnpike results obtained in our previous research, and describe the structure of the book.…”

Section: Introductionmentioning

confidence: 99%

Turnpike Theory of Continuous-Time Linear Optimal Control Problems

Zaslavski

2015

Springer Optimization and Its Applications

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Aims and ScopeOptimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics, and other sciences.The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository work that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multi-objective programming, description of software packages, approximation techniques and heuristic approaches.More information about this series at

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“…These optimal control problems are discrete-time analogs of Bolza problems in the calculus of variations. This is due not only to theoretical achievements in this area, but also because of numerous applications to engineering [1,15,24], models of economic dynamics [14,18,21,[23][24][25]29,30], the game theory [13,24,27], models of solid-state physics [3] and the theory of thermodynamical equilibrium for materials [16,17]. In this paper we study the structure of approximate solutions of problems (P) on large intervals.…”

Section: Introductionmentioning

confidence: 99%

Structure of approximate solutions of discrete time optimal control Bolza problems on large intervals

Zaslavski

2015

Nonlinear Analysis: Theory, Methods & Applications

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Turnpike Theorems for Markov Games

Cited by 49 publications

References 92 publications

Evolutionary, mean-field and pressure-resistance game modelling of networks security

Evolutionary, mean-field and pressure-resistance game modelling of networks security

Turnpike Theory of Continuous-Time Linear Optimal Control Problems

Structure of approximate solutions of discrete time optimal control Bolza problems on large intervals

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