Generalized multiple information structure
- Authors: Fedyanin D.N.1, Chkhartishvili A.G.1
-
Affiliations:
- V.A. Trapeznikov Institute of Control Sciences of RAS
- Issue: No 109 (2024)
- Pages: 6-20
- Section: Systems analysis
- URL: https://journal-vniispk.ru/1819-2440/article/view/284362
- DOI: https://doi.org/10.25728/ubs.2024.109.1
- ID: 284362
Cite item
Full Text
Abstract
A new model for describing agents' awareness is proposed that generalizes the known reflexion models in the following sense: the proposed model of generalized multiple awareness structures (GMAS) allows for different numbers of participants in agents' perceptions of the situation. Such structures are used to construct information control and can be used to control the dynamics of opinions in social networks and to improve safety in transportation systems even when agents do not know the total number of agents in the system, which is very common in real life but rarely considered in game theory and epistemic logic. In the article, a formal description of probabilistic and interval GMAS is given, and cases of their transformation as a result of observing the choice of actions by agents and as a result of receiving a message by them are considered. Formal definitions of information equilibrium for both types of GMAS are proposed, and the information equilibrium for probabilistic GMAS is formulated in such a way that it allows us to find Bayes –Nash equilibria.
About the authors
Denis Nikolaevich Fedyanin
V.A. Trapeznikov Institute of Control Sciences of RAS
Email: dfedyanin@inbox.ru
Moscow
Alexander Gedevanovich Chkhartishvili
V.A. Trapeznikov Institute of Control Sciences of RAS
Email: sandro_ch@mail.ru
Москва
References
- АЛГАЗИН Г.И., АЛГАЗИНА Д.Г. Моделирование дина-мики коллективного поведения в рефлексивной игре с произвольным числом лидеров // Информатика и автома-тизация. – 2022. – №21(2). – С. 339–375.
- НОВИКОВ Д.А. Теория управления организационными системами. – М.: ЛЕНАНД, 2022. – 500 с.
- НОВИКОВ Д.А., ЧХАРТИШВИЛИ А.Г. Рефлексивные игры. – М.: Синтег, 2003. – 160 с.
- НОВИКОВ Д.А., ЧХАРТИШВИЛИ А.Г. Рефлексия и управление: математические модели. – М.: Изд-во физю-мат. лит-ры, 2013. – 412 с.
- ЧХАРТИШВИЛИ А.Г. Об одной рефлексивной игре по-иска // Управление большими системами: сборник тру-дов. – 2003. Вып. 5. – С. 123–128.
- ЧХАРТИШВИЛИ А.Г. Рефлексивные игры: трансфор-мация структур информированности // Проблемы управления. – 2008. – №5. – С. 43–48.
- AGHASSI M., BERTSIMAS D. Robust game theory // Math-ematical programming. – 2006. – Vol. 107(1–2). – P. 231–273.
- AUMANN R.J., HEIFETZ A. Incomplete information // Handbook of game theory with economic applications. – 2002. – P. 1665–1686.
- FEDYANIN D.N. Threshold and Network generalizations of Muddy Faces Puzzle // Proc. of the 11th IEEE Int. Conf. on Application of Information and Communication Technolo-gies (AICT2017, Moscow). – M.: IEEE, 2017. – Vol. 1. – P. 256–260.
- FEDYANIN D.N. Logic for Chkhartishvili-Novikov Struc-tures of Beliefs // Int. Journal of Unconventional Computing. – 2020. – Vol. 15, Iss. 4. – P. 259–273.
- GALEAZZI P., LORINI E. Epistemic logic meets epistemic game theory: A comparison between multi-agent Kripke models and type spaces // Synthese. – 2016. – Vol. 193. – P. 2097–2127.
- HARSANYI J.C. Games with incomplete information // The American Economic Review. – 1995. – Vol. 85(3). – P. 291–303.
- JACKSON M.O., SIMON L.K., SWINKELS J.M., ZA-ME W.R. Communication and equilibrium in discontinuous games of incomplete information // Econometrica. – 2002. – Vol. 70(5). – P. 1711–1740.
- PEREA A. Epistemic Game Theory: Reasoning and Choice. Universiteit Maastricht, 2012. – 580 p.
Supplementary files
