Bifurcations and Nash Equilibria in Tilings

The Mathematics Department would like to invite you to the semi
nar
Bifurcations and Nash Equilibria in Tilings

Abdelrahim S. Mousa
As
sistant Professor at Mathematics Department

Homepage: https://sites.goog
le.com/a/ritaj.ps/abdelrahim-mousa/home

Time: 1:00-2:00 pm
Date: Marc
h 7, 2015 (Saturday)
Place: Faculty of Information Technology (Tec 109)

Abstract:

We study a dichotomous decision model, where individuals
can make the decision yes or no and can influence the decisions of others.
We characterize all decisions that form Nash equilibria. Taking into accoun
t the way individuals influence the decisions of others, we construct the
decision tilings where the axes reflect the personal preferences of the ind
ividuals for making the decision yes or no. These tilings characterize geom
etrically all the pure and mixed Nash equilibria. We show, in these tiling
s, that Nash equilibria form degenerated hysteresis with respect to the re
plicator dynamics, with the property that the pure Nash equilibria are asy
mptotically stable and the strict mixed equilibria are unstable. This hyste
resis can help to explain the sudden appearance of social, political and e
conomic crises. We observe the existence of limit cycles for the replicatordynamics associated to situations where the individuals keep changing thei
r decisions along time, but exhibiting a periodic repetition in their deci
sions.
References
[1] A. S. Mousa, R. Soeiro, T. R. Oliveira and A. A.
Pinto. Dynamics of Human Decisions, Journal of Dynamics and Games, v1(1)
, 1-31, (2012).
[2] L. Almeida, J. Cruz, H. Ferreira and A. Pinto. Baye
sian-Nash Equilibria in Theory of Planned Behavior, Journal of Difference
Equations and Applications, 17, 1085-1093, (2011).
[3] J. Conley and M.Wooders. Tiebout Economies with Differential Genetic Types and Endogenousl
y Chosen Crowding Characteristics, Journal of Economic Theory, 98, 261-2
94, (2001).
[4] 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).