  We have studied an evolutionary game with spatially arranged players who can
choose one of the two strategies (named cooperation and defection for social
dilemmas) when playing with their neighbors. In addition to the application of
the usual strategies in the present model the players are also characterized by
one of the two extreme personal features representing the egoist or fraternal
behavior. During the evolution each player can modify both her own strategy
and/or personal feature via a myopic update process in order to improve her
utility. The results of numerical simulations and stability analysis are
summarized in phase diagrams representing a wide scale of spatially ordered
distribution of strategies and personal features when varying the payoff
parameters. In most of the cases only two of the four possible options prevail
and may form sublattice ordered spatial structure. The evolutionary advantage
of the fraternal attitude is demonstrated within a large range of payoff
parameters including the region of prisoner's dilemma where egoist defectors
and fraternal cooperators form a role-separating chessboard-like pattern.
