Informatics and Applications
2024, Volume 18, Issue 2, pp 2-8
ON FUNCTOR REPRESENTATION OF OPTIMIZED DYNAMIC MULTIAGENT SYSTEMS
Abstract
Functors' topoi is chosen as a computational tool for synthesizing dynamic multiagent systems (DMAS).
The scale orders the objects as multiagent system states to solve attendant static subgames in them. The initial dynamic game and all static subproblems are represented in the monoidal category of binary relations. Players' preference relations might be maximized in DMAS. The game rational solution is understood as equilibrium. The compositional structure of the optimized DMAS can be described in the form of the game dynamic resulting relation (DRR). Players' rational behavior search is reduced to DRR subsequent maximization. For this purpose, the Bellman's method is generalized to solve control problems stated in the form of relations. The program implementation of the approach can be based on neural networks due to the consistency of the architectures of the applied relation graphs and neural networks.
[+] References (13)
- Moiseev, N. N. 1975. Elementy teorii optimal'nykh sistem [Elements of optimal systems theory]. Moscow: Nauka. 527 p.
- Germeyer, Yu. B. 1976. Igry s neprotivopolozhnymi interesami [Games with nonopposing interests]. Moscow: Nauka. 326 p.
- Krasovskiy, N. N., and A. I. Subbotin. 1974. Pozitsionnye differentsial'nye igry [Positional differential games]. Moscow: Nauka. 456 p.
- Dockner, E. J., S. Jorgensen, N. V. Long, and G. Sorger. 2000. Differential games in economics and management science. Cambridge: Cambridge University Press. 382 p. doi: 10.1017/CBO9780511805127.
- Vasilyev, N. S. 2023. Kompozitsional'noe predstavlenie struktury igry mnogikh lits v monoidal'noy kategorii binarnykh otnosheniy [Multiplayers' games compositional structure in the monoidal category of binary relations]. In - formatika i ee Primeneniya - Inform. Appl. 17(2):18-26. doi: 10.14357/19922264230203. EDN: GPMZTS.
- Dixit, A. K., and B. J. Nalebuff. 2008. The art of strategy. New York, London: W W Norton & Co. 446 p.
- Shoham, Y., and R. Leyton-Brown. 2010. Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press. 532 p.
- Bai, Q., F Ren, K. Fujita, and M. Znang. 2016. Multiagent and complex systems. Studies in computational intelligence ser. Springer Singapore. 210 p.
- Dixit, A. K., S. Skeath, and D. H. Reiley, Jr. 2017. Games of strategy. New York, London: W.W. Norton & Co. 880 p.
- Skornyakov, L. A. 1983. Elementy obshchey algebry [Elements of general algebra]. Moscow: Nauka. 272 p.
- Mac Lane, S. 1998. Categories for the working mathematician. 2nded. New York, NY: Springer. 318 p.
- Gubko, M. V. 2004. Control of organizational systems with network interaction of agents. II. Stimulation problems. Automat. Rem. Contr. 65(9):1470-1485. doi: 10.1023/B:AURC.0000041425.34118.7d. EDN: LFMUCG.
- Demange, G., andM. Wooders, eds. 2005. Group formation in economics: Networks, clubs, and coalitions. Cambridge: Cambridge University Press. 475 p.
[+] About this article
Title
ON FUNCTOR REPRESENTATION OF OPTIMIZED DYNAMIC MULTIAGENT SYSTEMS
Journal
Informatics and Applications
2024, Volume 18, Issue 2, pp 2-8
Cover Date
2024-06-20
DOI
10.14357/19922264240201
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
functor category; compositionality; monoidal category; opposite image; game dynamic relation; static subgame; preference relation; dynamic resulting relation; rational solution; Bellman morphism
Authors
N. S. Vasilyev 
Author Affiliations
N. E. Bauman Moscow State Technical University, 5-1 Baumanskaya 2nd Str., Moscow 105005, Russian Federation
|