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.
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.