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Mathematics
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Multi-Agent Systems of Competitive and Cooperative Interaction
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Multi-Agent Systems of Competitive and Cooperative Interaction

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 4439

Special Issue Editor

Prof. Dr. Oleg Malafeyev

E-Mail Website
Guest Editor
Faculty of Applied Mathematics and Control Processes, Department of Mathematical Modeling, St. Petersburg University, St. Petersburg, Russia
Interests: stochastic system; forward-backward stochastic differential equations; aggregative games

Special Issue Information

Dear Colleagues,

Multi-agent controlled systems are formalized, whereby a finite (or infinite) number of participants (components) of the considered multi-agent process enter into competitive or cooperative interaction with each other. The questions of realizability of various game-theoretic principles of optimality of a competitive or cooperative type are investigated. Questions of the strategic stability of these principles of optimality under certain restrictions are also studied. Models with a large number of players are often useful to analyze in the statistical limit of an infinite number of particles, which makes it possible to turn the “curse of high dimensionality” into a “blessing of high dimensionality”. The applications of the studied models are very multifaceted. They naturally arise when considering a variety of socio-economic processes, including models of inspection, corruption, the fair distribution of resources, the pricing of gambling options, the planning of long-term projects on a competitive basis, etc.

Prof. Dr. Oleg Malafeyev
Guest Editor

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Keywords

  • pricing of gambling options
  • socio-economic processes
  • game-theoretic principles of optimality
  • competitive and cooperative interaction
  • multi-agent controlled systems

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Published Papers (3 papers)

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Research

26 pages, 1992 KiB  
Article
Pursuit Problem of Unmanned Aerial Vehicles
by Malafeyev Oleg and Kun Zhang
Mathematics 2023, 11(19), 4162; https://doi.org/10.3390/math11194162 - 4 Oct 2023
Viewed by 1506
Abstract
The study examines scenarios involving a single pursuer tracking a single evader, as well as situations where multiple pursuers are involved in chasing multiple evaders. We formulate this problem as a search and pursuit problem for unmanned aerial vehicles (UAVs). Game theory offers [...] Read more.
The study examines scenarios involving a single pursuer tracking a single evader, as well as situations where multiple pursuers are involved in chasing multiple evaders. We formulate this problem as a search and pursuit problem for unmanned aerial vehicles (UAVs). Game theory offers a mathematical framework to model and examine strategic interactions involving multiple decision-makers. By employing game theory principles to address the search and pursuit problem, our objective is to optimize the efficiency of strategies for detecting and capturing unmanned aerial vehicles (UAVs). Full article
(This article belongs to the Special Issue Multi-Agent Systems of Competitive and Cooperative Interaction)
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15 pages, 329 KiB  
Article
On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals
by Alexandra Borodina and Vladimir Mazalov
Mathematics 2023, 11(16), 3535; https://doi.org/10.3390/math11163535 - 16 Aug 2023
Cited by 1 | Viewed by 1217
Abstract
This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. [...] Read more.
This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. In addition, each customer entering the system uses a strategy and must independently decide when to arrive in the system within a fixed admission period of time so that the expected sojourn time is minimal. We interpret the arrival process as a Nash equilibrium solution of a noncooperative game when the arrival intensity is completely described by an unknown distribution function, and then we propose a way to find an equilibrium for the case when the client’s waiting time for service is obviously limited. The analytical solution for the equilibrium is illustrated numerically for two-person and three-person games. Full article
(This article belongs to the Special Issue Multi-Agent Systems of Competitive and Cooperative Interaction)
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11 pages, 271 KiB  
Article
On Effective Fine Functions for Inspection—Corruption Games (Evolutionary Approach)
by Vassili N. Kolokoltsov and Dmitri V. Vetchinnikov
Mathematics 2023, 11(15), 3429; https://doi.org/10.3390/math11153429 - 7 Aug 2023
Viewed by 1167
Abstract
In previous papers of the authors, a generalized evolutionary approach was developed for the analysis of popular inspection and corruption games. Namely, a two-level hierarchy was studied, where a local inspector I of a pool of agents (that may break the law) can [...] Read more.
In previous papers of the authors, a generalized evolutionary approach was developed for the analysis of popular inspection and corruption games. Namely, a two-level hierarchy was studied, where a local inspector I of a pool of agents (that may break the law) can be corrupted and is further controlled by the higher authority A. Here, we extend this two-level modeling by answering the following questions: (i) what levels of illegal profit r of violators and what level of bribes α (fraction of illegal profit asked as a bribe from a violator) of an inspector are feasible, that is, realizable in stable equilibria of generalized replicator dynamics; and (ii) what α can be optimal for a corrupted inspector that aims at maximizing the total profit. Concrete settings that we have in mind are illegal logging, the sales of products with substandard quality, and tax evasion. Full article
(This article belongs to the Special Issue Multi-Agent Systems of Competitive and Cooperative Interaction)
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