Abstract
This work is focused on the use of linear games in the normal form for evaluation of Nash equilibria probability distribution in spatial data eg land use. Spatial data with varied content represent the observed state and, as a rule, do not automatically offer information about what that state is the result of. However, individual cases can be defined in such data, representing, for example, different sizes or degrees of representation of selected characteristics. The essence of the proposed approach is that such data pertaining to individual cases are regarded as payoff values of multiple interacting entities and can form a matrix of a symmetric linear game in the normal form. For this game, an NE representing a particular distribution of strategies of interacting entities can then be determined. This distribution assigns to each case the share of NE depending on the respective location in the symmetric game matrix. However, spatial data does not provide any information for the specific design of this deployment. The proposed solution is therefore stochastic: all effective permutations of the game matrix or a multidimensional symmetric game configuration leading to a different result for the NE distribution are evaluated. The result are values of the occurrence of NE probability for individual evaluated cases. The properties of the method are tested on the example of a practical application. The results show that the method is applicable for evaluating the spatial distribution of the land use stability.
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This study was supported by projects 19-24089J funded by Czech Science Foundation.
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Appendix
Availability and implementation—the calculation for up to 32 dedicated cases and a maximum of 5 interacting entities can be practically done on the equsis.com. Development version (FORTRAN codes of computational subroutines) is available at github.com/vachm/equsis.
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Vach, M. A game-theoretic approach for stochastic estimation of equilibrium in land use data: stochastic estimation of equilibrium in land use data. Stoch Environ Res Risk Assess 34, 2107–2124 (2020). https://doi.org/10.1007/s00477-020-01873-2
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DOI: https://doi.org/10.1007/s00477-020-01873-2