Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31106
Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space

Authors: A. S. Mousa, F. Shoman

Abstract:

We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: Game theory, Nash Equilibrium, coherent strategy, split strategy, pure strategy, mixed strategy

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 172

References:


[1] I. Ajzen. Perceived behavioral control, self-efficacy, locus of control, and the theory of planned behavior. Journal of Applied Social Psychology, 32:665–683, 2002.
[2] L. Almeida, J. Cruz, H. Ferreira, and A. A. Pinto. Bayesian-Nash equilibria in theory of planned behavior. Journal of Difference Equations and Applications, 17:1085–1093, 2011.
[3] J. Brida, M. Defesa, M. Faias, and A. A. Pinto. Strategic choice in tourism with differentiated crowding types. Economics Bulletin, 30:1509–1515, 2010.
[4] J. P. Conley and M. H. Wooders. Tiebout economies with differential genetic types and endogenously chosen crowding characteristics. Journal of Economic Theory, 98:261–294, 2001.
[5] A. S. Mousa, M. Faias, and A. A. Pinto. Resort pricing and bankruptcy. In Peixoto M., Pinto A., and Rand D., editors, Dynamics, Games and Science II, volume 2 of Proceedings in Mathematics series, chapter 40, pages 567–573. Springer-Verlag, German, 2011.
[6] A. S. Mousa, M. S. Mousa, R. M. Samarah, and A. A. Pinto. Tilings and bussola for making decisions. In Peixoto M., Pinto A., and Rand D., editors, Dynamics, Games and Science I, volume 1 of Proceedings in Mathematics series, chapter 44, pages 689–708. Springer-Verlag, 2011.
[7] A. S. Mousa, D. Pinheiro, and A. A. Pinto. A consumption-investment problem with a diminishing basket of goods. In Almeida J. P., Oliveira J. F., and Pinto A. A., editors, Operational Research: IO 2013 - XVI Congress of APDIO, CIM Series in Mathematical Sciences, chapter 17, pages 295–310. Springer, 2015.
[8] 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, 67:133–144, 2016.
[9] A. S. Mousa and A. A. Pinto. Geometric approaches and bifurcations in the dichotomous decision model. Journal of the Arab American University, 3(2):10–39, 2017.
[10] A. S. Mousa, A. A. Pinto, and R. Soeiro. Influence of Individual Decisions in Competitive Market Policies. Mathematics of Planet Earth. Editora Universitria do Instituto Superior Tcnico, IST Press, Lisboa, Portugal, 2014.
[11] A. S. Mousa, R. Rajab, and A. A. Pinto. Characterizing the geometry of envy human behaviour using game theory model with two types of homogeneous players. International Journal of Mathematical and Computational Sciences, 14(5):45 – 52, 2020.
[12] R. Soeiro, A. S. Mousa, T. Oliveira, and A. A Pinto. Dynamics of human decisions. Journal of Dynamics and Games, 1(1):1–31, 2012.
[13] R. Soeiro, A. S. Mousa, and A. A. Pinto. Externality effects in the formation of societies. Journal of Dynamics and Games, 2:303–320, 2015.