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Title: Characterizing the geometry of envy human behaviour using game theory model with two types of homogeneous players
Authors: Mousa, Abdelrahim 
Rajab, Reem 
Pinto, Alberto 
Keywords: Game theory;Tiling (Mathematics);Noncooperative games (Mathematics);Geometric tilings;Bifurcation theory;Noncooperative games (Mathematics);Nash Equilibrium;Envy Nash Equilibrium
Issue Date: 20-May-2020
Publisher: World Academy of Science, Engineering and Technology
Journal: International Journal of Mathematical and Computational Sciences 
Abstract: An envy behavioral game theoretical model with two types of homogeneous players is considered in this paper. The strategy space of each type of players is a discrete set with only two alternatives. The preferences of each type of players is given by a discrete utility function. All envy strategies that form Nash equilibria and the corresponding envy Nash domains for each type of players have been characterized. We use geometry to construct two dimensional envy tilings where the horizontal axis reflects the preference for players of type one, while the vertical axis reflects the preference for the players of type two. The influence of the envy behavior parameters on the cartesian position of the equilibria has been studied, and in each envy tiling we determine the envy Nash equilibria. We observe that there are 1024 combinatorial classes of envy tilings generated from envy chromosomes: 256 of them are being structurally stable while 768 are with bifurcation. Finally, some conditions for the disparate envy Nash equilibria are stated.
Description: Article published in : International Journal of Mathematical and Computational Sciences, vol. 14, no. 6, 2020
ISSN: ISSN : 1307-6892
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