Characterizing the Geometry of Envy Human Behaviour Using Game Theory Model with Two Types of Homogeneous Players

Authors: A. S. Mousa, R. I. Rajab, A. A. Pinto

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.

Keywords: Game theory, Nash Equilibrium, envy Nash Equilibrium, geometric tilings, bifurcation thresholds.

References:

[1] I. Ajzen, Perceived behavioral control, self-efficacy, locus of control, and the theory of planned behavior, Journal of Applied Social Psychology, 32 (2002), 665–683.
[2] J. G. Brida, M. J. Such-devesa, M. Faias and A. A. Pinto, Strategic choice in tourism with differentiated crowding types, Economics Bulletin, 30 (2010), 1509–1515.
[3] L. Almeida, J. Cruz, H. Ferreira and A. A. Pinto, Bayesian-Nash equilibria in theory of planned behaviour, Journal of Difference Equations and Applications, 17 (2011), 1085–1093.
[4] J. P. Conley and M. H. Wooders, Tiebout economies with differential genetic types and endogenously chosen crowding characteristics, Journal of Economic Theory, 98 (2001), 261–294.
[5] R. Soeiro, A. Mousa, T. R. Oliveira and A. A. Pinto, Dynamics of human decisions, Journal of Dynamics and Games, 1 (2014), 121–151.
[6] R. Soeiro and A. S. Mousa and A. A. Pinto, Externality effects in the formation of societies, Journal of Dynamics and Games, 2 (2015), 303–320.
[7] A. S. Mousa and A. A. Pinto, Geometric approaches and bifurcations in the dichotomous decision model, Journal of the Arab American University, 3 (2017), 10–39.
[8] A. S. Mousa and M. Faias and A. A. Pinto, Resort pricing and bankruptcy, Dynamics, Games and Science II, Editors: Peixoto M. and Pinto A. and Rand D, Proceedings in Mathematics series, Springer-Verlag, V2, Ch40, (2011), 567–573.
[9] A. S. Mousa, M. S. Mousa, R. M. Samarah and A. A. Pinto, Tilings and bussola for making decisions, Dynamics, Games and Science I, Editors: M. Peixoto, A. A. Pinto and D. Rand, Proceedings in Mathematics series, Springer-Verlag, V1, Ch44, (2011), 689–708.
[10] A. S. Mousa, D. Pinheiro and A. A. Pinto, A consumption-investment problem with a diminishing basket of goods, Operational Research: IO 2013 - XVI Congress of APDIO, Editors: J. P. Almeida, J. F. Oliveira and A. A. Pinto, CIM Series in Mathematical Sciences, Springer-Verlag, Ch17, (2015), 295–310.
[11] A. S. Mousa, D. Pinheiro and A. A. Pinto, Optimal life insurance purchase from a market of several competing life insurance providers, Insurance: Mathematics and Economics, 67 (2016), 133–144.