Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space

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.

Authors:

• A. S. Mousa
• F. Shoman

Keywords:

• Coherent strategy
• split strategy
• pure strategy
• mixed strategy
• Nash Equilibrium
• game theory.

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.