Graphs for the Replicator Equations and the “Tragedy of the Exhaustion of the Common Resource”

Active users have appeared who require the solution of inverse problems on a graph with conditions of uncertainty for modeling processes in the economic sphere. Such tasks were not considered by mathematicians earlier. This article provides an analogy with mathematical models which are described by...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2020-03, Vol.12 (2), p.246-256
Main Authors: Volosova, N. K., Volosova, A. K., Volosov, K. A., Vakulenko, S. P.
Format: Article
Language:English
Subjects:
Asymptotic methods
Boundary layers
Economic models
Exhaustion
Inverse problems
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Simulation and Modeling
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Summary:Active users have appeared who require the solution of inverse problems on a graph with conditions of uncertainty for modeling processes in the economic sphere. Such tasks were not considered by mathematicians earlier. This article provides an analogy with mathematical models which are described by a replicator system (RS) of equations related to the stated theme. The exact and asymptotic solutions are developed in the case of “stiff” RS equations. The effects of an a priori dying clone and of the boundary layer for small values of time are found. An analogy is drawn with some objects having similar features, which really exist in the economy. The effect of the existence of shadow, invisible super-consumers is described.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048220020167