\r\ntypes of homogeneous players is considered in this paper. The

\r\nstrategy space of each type of players is a discrete set with only

\r\ntwo alternatives. The preferences of each type of players is given

\r\nby a discrete utility function. All envy strategies that form Nash

\r\nequilibria and the corresponding envy Nash domains for each type

\r\nof players have been characterized. We use geometry to construct

\r\ntwo dimensional envy tilings where the horizontal axis reflects the

\r\npreference for players of type one, while the vertical axis reflects

\r\nthe preference for the players of type two. The influence of the envy

\r\nbehavior parameters on the Cartesian position of the equilibria has

\r\nbeen studied, and in each envy tiling we determine the envy Nash

\r\nequilibria. We observe that there are 1024 combinatorial classes of

\r\nenvy tilings generated from envy chromosomes: 256 of them are

\r\nbeing structurally stable while 768 are with bifurcation. Finally, some

\r\nconditions for the disparate envy Nash equilibria are stated.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 162, 2020"}