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 Âûïóñê 55
- Ougolnitsky G. Preface
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- Astrakhantsev G., Menshutkin V., Minina T. Assimilative capacity estimate generation using models of great lakes’ ecosystems
The mathematical modeling framework of lakes’ ecosystems (with Ladoga and Onega lakes serving as examples) was developed for more than 25 years by Professor L.A. Rukhovets and his team with main results published in the leading Russian and worldwide scientific journals and monographs. Development of economic mechanisms of water use management for large stratified lakes is a natural extension of these studies. We consider the abilities of existing mathematical models for numeric estimates of assimilation capacity of the greatest freshwater lakes.
- Breer V., Novikov D., Rogatkin A. Models of collective threshold behavior in control problems of ecological-economic systems
We study models of collective “multi-threshold” behavior of agents making binary decisions. The general analysis scheme of these models is applied to three control problems of ecological-economic systems, namely, the problem of individual penalties, the problem of individual and collective penalties, as well as to the incentive problem of agents’ investments in environmental protection and/or restoration.
- Burkov V., Burkova I., Puzyrev S. The principle of coordinated planning in the management of social and ecological-economic systems
We consider a problem of managing distributed projects and programs. Such a program consists of routines distributed either functionally and administratively, or geographically. For example, a program of region development includes a subprogram of environmental safety. The main challenge in managing distributed programs is the problem of interests’ reconciliation of all stakeholders. We propose the principle of coordinated planning for plan development of a distributed program.
- Voronin A., Vasilchenko A., Pisareva M., Pisarev A., Khoperskov A., Khrapov S., Podschipkova J. Designing a system for ecological–economical management of the volga–akhtuba floodplain on basis of hydrodynamic and geoinformational simulation
A system is introduced for ecological-economical management of the territory of the Volga-Akhtuba floodplain. The system is built on the basis of hydrodynamic computer simulations and geo-informational technologies. We optimize the flood hydrograph for the Volga hydroelectric station, suggest the optimal plan of the system of channels for Volga-Akhtuba floodplain recovery, and develop control mechanisms for local economic entities.
- Gorelik V. Correction of cooperative games as stabilization mechanism of ecological-economic systems
An approach is suggested for decision-making problems where players’ preferences result in the empty core of the cooperative game. The approach is based on a minimal correction of the initial model. We illustrate the idea on the cooperative game in the form of characteristic function with the empty core originated from the model of an unsustainable ecological-economic system, for which a correction is interpreted as a stabilization mechanism. We introduce the concept of Cp-core and explain its calculation.
- Gorelik V., Zolotova T. Hierarchical regional models of environment protection
We study a fan-shaped hierarchical system with one top-level element and n elements at the lower level. Necessary and sufficient conditions for the optimal strategy of the upper level are formulated, which are used to study a hierarchical model of regional environmental protection. Several control mechanisms for environmental payments, limits, and penalties are suggested, which allow perfect coordination of interests of the upper and lower hierarchical levels.
- Gromova E., Petrosyan L. Strongly time-consistent cooperative solution for a differential game of pollution control
In this paper an approach to the determination of the strongly time-consistent cooperative solution for differential games with 2 players is proposed. This approach allows to construct a cooperative solution satisfying strongly time-consistency property under rather general conditions. It is shown that the obtained solution also satisfies the condition of irrational behaviour proofness. The obtained game-theoretical results are illustrated by differential game of pollution control.
- Gurman V., Dameshek L., Konstantinov G., Nasatueva S., Rasina I., Chemesova T. Quoting anthropogenic environmental impacts on the basis of ecological and economic models
We briefly survey the mathematical models of ecologicaleconomical and social-ecological-economical systems and introduce an approach to the problem of implementation of regional sustainable development, which is related to the game-theoretic philosophy, and consists in assigning quotas on anthropogenic impact. We consider a system as heterogenous one and suggest appropriate mathematical tools.
- Zakharov V., Krylatov A. Competitive green vehicles assignment in transportation network
Nowadays there is a lack of methodological tools for supporting decision makers in the sphere of motivation to use green vehicles by drivers and of available green capacity allocation. We study the problem of green and non-green traffic flow assignment in the network consisting of green and non-green routes. The analysis of competitive and cooperative frameworks is performed. We suggest an approach to green routes’ selection (defining the, so called, green subnetwork, which is fully loaded and provides smaller travel time for green vehicles under Wardrop and Nash traffic flow assignments). We also elicit explicit balancing conditions for the green subnetwork in case of parallel routes.
- Ivanko N., Abakumov A. Fishery control problem with quotas
We study several models of fishery control with catch quotas. Alternative linear approximations of initial non-linear problems are suggested along with linearized routines for their study. We also suggest game-theoretic models of fishery and consider illustrative examples for optimal quota assignment problem and for the maximal profit problem.
- Ivanova A., Kirillov A. Equilibrium and control in the problem of species composition protection in biocommunity
The mathematical models are proposed for the problem of a biological community species composition protection. The equilibrium is constructed for the dynamical model, describing the self regulation of the populations presence in a patch. For the model with varying food attractiveness we find species removal limits, which allow preserving the species composition.
- Il’ichev V., Dashkevich L., Kulygin V. Evolutionary stable characteristics of sea of azov with variations of don river runoff
An ecological evolutionary simulation for the system “biogenic elements – algae” is introduced. It is found that in the asymptotic mode the relation of organic forms of nitrogen and phosphorus in the ecosystem varies slightly, despite the strong deformation of the chemical composition of the runoff of the Don river. We perform a series of “paradoxical” model experiments to uncover the reason of this phenomenon. We also determine the evolutionary stable values of the temperature, which is favorable for the growth of main algae groups. It is shown that for the thermophilic algae such a temperature is unique, while for cold-loving algae two favorable values of the temperature are possible.
- Mazalov V., Rettieva A. Asymmetry in a cooperative bioresource management problem
Discrete-time game-theoretic models related to a bioresource management problem (fishery) with asymmetric players are investigated. Players use different discount factors and have different random planning horizons. The main goal here is to construct the value function for the cooperative solution and to distribute the joint payoff among the players in asymmetric cases. We propose using the Nash bargaining solution to obtain cooperative profits and strategies. It is shown that cooperative behavior determined by bargaining schemas is not the only profitable one for players but is better for ecology.
- Nazirov A., Ougolnitsky G., Usov A. Game-theoretical model of three-level marketing system considering environmental requirements
A novel mathematical model is introduced to express activities of parties in a vertical marketing system. The parties are represented with a manufacturer, a mediator, and a trading enterprise. The relationship between the manufacturer and the mediator is governed by a commission contract. The manufacturer produces goods while the mediator represents her interests to the trading enterprise, and the trading enterprise sells products. The model is based on the game-theoretic and hierarchical approaches. A Stackelberg equilibrium considering the requirements of sustainable development is found. The impulsion method is used as a tool of hierarchical control when solving this model. A number of typical examples followed by the interpretation are presented.
- Nikitina A., Puchkin M., Semenov I., Sukhinov A., Ougolnitsky G., Usov A., Chistyakov A. Differential game of fish kill prevention in shallow waterbodies
We build and investigate a differential game of fish kill prevention in shallow waterbodies. The algorithms are suggested for information structures Ã1x and Ã2x in dynamic Germeier games. The problem is solved numerically by the developed parallel algorithm, which considers the structure of a supercomputer with distributed memory. The proposed algorithm uses the k-means method and essentially reduces calculation time. The above models and routines are used to forecast the change in biomass volume of biological populations in shallow waterbodies considering the requirements of sustainable development.
- Novikov D., Chkhartishvili A. Models of reflexive games in control problems of ecological-economic systems
We substantiate the feasibility and reasonability of employing the framework of reflexive games for describing decision-making and control problems of ecological-economic systems.
- Shchepkin A. Analysis of a quota trading mechanism
We study the model of regional environmental safety, when a Principal (the local government) sales environmental risk quotas to enterprises being the source of potential ecological danger. The total volume of risk quotas is limited. We suggest a quota assignment mechanism for the case when the total volume of bids exceeds the predefined total quota volume. We study the model when enterprises bye the quotas while a Principal performs monitoring of a real safety level in production and compares it with quotas sold.
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