Game strategies for decision making in hierarchical systems. II. Computer simulation of stochastic game

Authors

  • Petro A. Kravets Lviv Polytechnic National University, Lviv, Ukraine

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2019.4.11

Keywords:

decision making, hierarchical system, conditions of uncertainty, stochastic game, computer modelling

Abstract

An algorithm for solving a stochastic game for decision making in hierarchical systems under uncertainty is developed. An analysis of the results of computer modeling of a stochastic game for autocratic, anarchic and democratic hierarchical decision making systems with the binary tree structure is performed. It has been established that autocratic-centric hierarchical systems have the smallest training time for achieving a close-to-consensus solution. The influence of parameters on the convergence of the game method in the process of finding a consensus or a majoritarian collective solution is studied.

Author Biography

Petro A. Kravets, Lviv Polytechnic National University, Lviv

Petro Alekseevich Kravets,

Cand. Tech. Sci. (Ph.D.), an associate professor at the Department of Information Systems and Networks of Lviv Polytechnic National University, Lviv, Ukraine.

Research areas: game models and decision-making methods under conditions of uncertainty, multi-agent systems.

References

Hierarchies in Distributed Decision Making / Christoph Schneeweiss. — Springer, 2013. — 341 p.

Nedashkivs'ka N.I. Metodolohija ta instrumentarij pidtrymky pryjnjattja rishen' na osnovi iyerarkhichnykh ta merezhevykh modelej: dys. … doktora tekhn. nauk: 01.05.04 / N. I. Nedashkivs'ka. — K.: NNK "IPSA" NTUU "KPI", 2018. — 407 s. — [Digital source]. — Available at: http://ela.kpi.ua/bitstream/123456789/25119/1/Nedashkivska_diss.pdf.

Kravets' P.O. Ihrova model' pryjnjattja rishen' v iyerarkhichnykh systemakh / P.O. Kravets' // Informatsijni systemy ta merezhi: visn. NU "L'vivs'ka politekhnika". — 2017. — № 872. — S. 111–120.

Kravets' P.O. Ihrova model' systemy z avtorytarnym pryjnjattjam rishen' / P.O. Kravets' // Informatsijni systemy ta merezhi: visn. NU "L'vivs'ka politekhnika". — 2018. — № 901. — S. 61–67.

Germejer Ju.B. Igry s neprotivopolozhnymi interesami / Ju.B. Germejer. — M.: Nauka, 1976. — 328 s.

Harrington J. E., Jr. Games, Strategies, and Decision Making / J.E. Harrington, Jr. — Worth Publishers, 2014. — 540 p.

Grabisch M. Set Functions, Games and Capacities in Decision Making / M. Grabisch. — Springer, 2016. — 473 p. — DOI: 10.1007/978-3-319-30690-2.

Ummels M. Stochastic Multiplayer Games: Theory and Algorithms / M. Ummels. — Amsterdam University Press, 2014. — 174 p.

Petrosjan L.A. Game Theory and Application / L.A. Petrosjan, V.V. Mazalov. — Nova Science Publishers, 2002. — 295 p.

Ungureanu V. Pareto-Nesh-Stackelberg Game and Control Theory: Intelligent Paradigms and Applications / V. Ungureanu. — Springer, 2018. — 343 p.

Wooldridge M. An Introduction to Multiagent Systems / M. Wooldridge. — John Wiley & Sons, 2009. — 461 p.

Radley N. Multi-Agent Systems – Modeling, Control, Programming, Simulations and Applications / N. Radley. — Scitus Academics LLC, 2017. — 284 p.

Iterative Learning Control for Multi-agent Systems Coordination / S. Yang, J.-X. Xu, X. Li, D. Shen. — John Wiley & Sons, 2017. — 272 p.

Sun Z. Cooperative Coordination and Formation Control for Multi-agent Systems / Zhiyong Sun. — Springer, 2018. — 179 p.

Agent for Games and Simulations: Trends in Techniques, Concepts and Design / F. Dignum, J.Bradshaw, B. G. Silverman, W. van Doesburg. — Springer, 2009. — 237 p.

Bekker K. The Guide to Computer Simulation and Games / K. Bekker, J.R. Parker. — John Wiley and Sons, 2011. — 456 p.

Simulation of Decision-Making as Active Learning Tools: Design and Effects of Political Science Simulations / P.Bursens, V. Donche, D. Gijbels, P. Spooren (Editors). — Springer, 2018. — 206 p.

Nazin A.V. Adaptivnyj vybor variantov / A.V. Nazin, A.S. Poznjak. — M.: Nauka, 1986. — 288 s.

Kushner H. Stochastic Approximation and Recursive Algorithms and Applications / H. Kushner, G. G. Yin. — Springer Science & Business Media, 2013. — 417 p.

Benveniste A. Adaptive Algorithms and Stochastic Approximations / A. Benveniste, M. Metivier, P. Priouret. — Springer Science & Business Media, 2012. — 365 p.

Published

2019-12-23

Issue

Section

Mathematical methods, models, problems and technologies for complex systems research