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 Выпуск 67
- Gorelov M. Maximal guaranteed result in hierarchical games
A new method of investigation of hierarchical two-player games is discussed. This method consists of solving games with complex information exchanges using, for the most part, identical transformation of predicate calculus formulas. We introduce the notion of maximal guaranteed result in a game, give two definitions and discuss the relationship between them. The new method is illustrated on a classical example for which a maximal guaranteed result of a high level player in hierarchical game of two players is calculated. Some particular cases are discussed. Stability of this problem according to variation of the payoff function of the second player is analyzed. We also demonstrate how the definition, and, accordingly, the method are modfied for a benevolent or a bounded-rational second player. Also, we show that the new definiton is convenient for the investigation of stability of maximal guaranteed result calculation procedure with respect to the parameters of the game.
- Boichenko V. Anisotropy-based analysis for case of nonzero initial condition
Well-known H_2-norm- and H_\infty-norm-theories allow construction of optimal regulators that minimize external disturbances' influence on the linear time-idependent system output. They are based on quality criteria of H_2- and H_\infty-norms of closed-loop transfer functions. In anisotropy theory, a notion of anisotropy norm is introduced. Usually in the context of the anisotropy-based robust performance analysis stochastic systems with zero initial condition are investigated. In this paper we extend this analysis and consider a linear discrete time invariant system under random disturbances and with the nonzero initial condition. In accordance with the basic postulates of the anisotropy-based control theory, the disturbance attenuation capabilities of system are quantified by the anisotropic generalized gain which is defined as the largest root mean square gain of the system with respect to a random input and the nonzero initial condition, anisotropy of which is bounded by a given nonnegative parameter a. A numerical example is considered.
- Akinfiev V. A model of competition between oil companies with conventional and unconventional oil production
This paper examines the problem of investment strategies choice of oil companies with conventional and unconventional oil production. A mathematical model describing the relationship between the oil companies’ investment strategies and the oil price, which depends on the ratio of supply and demand on the world oil market, is constructed and discussed. Solution is reduced to the analysis of a bimatrix game, where in the payoff matrix is formed by numerical simulation. Two possible scenarios of play are presented, a stable one and a volatile one. We present an illustrative example of the proposed approach. The obtained results show that unconven-tional oil production, including shale oil, will occupy a significant portion of the market in the medium term. Average market price of oil is expected to reach 55-60 $ per barrel. This model, however, does not account for possible technology advancements, which could lower the expense of oil extraction and, thus, market price.
- Ratner S. Dynamic problems of estimation of ecological-economic efficiency of regions based on basic models of data envelopment analysis
The paper describes the results of the comparative analysis of the applicability of several methods for solving dynamic DEA-models to the problem of monitoring of the ecological and economic efficiency of economic activities of regional economic systems (on the example of the regions of the Central Federal District, notably Belgorod and Ryazan regions). Methods of forming time series based on point estimates of environmental and economic efficiency, the Malkmquist method and the window method are considered. The results obtained for different window widths are analyzed for stability and adequacy. A comparison of the obtained results allows us to conclude that the window method is uniquely preferable for solving problems of monitoring the ecological and economic efficiency of regions not only from a computational but also from a substantive point of view. Unlike in case of Malkmquist method, system dynamics are more evident, and conclusions can be more easily drawn about the overall direction of the process. Data and graphs used in the comparison are also provided.
- Vasilyev M. About mathematical model of the capacity market
The capacity market in Russia is considered as an optimization model which is aimed at reaching minimum electricity supply costs for consumers. It is shown that the linear model applied to the discrete problem often does not reach optimum solution. The calculation is done for an abstract example and compared with the results of the discrete model. Competitive power output model solves an optimization problem which is, by its nature, discrete. Current model, either before 2015 (completely inelastic fixed demand) or after (demand depending on price), is a variant of linear programming problem, and thus does not always yield a true optimal solution. Substituting it for a discrete programming problem allows us to find better solutions and to lower costs for all involved power stations. Besides, in this framework we can accout for bandwidth limitations without subdividing price zones, which is especially relevant for Russian power systems. Further directions of research are proposed.
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