  Darwin's theory of evolution - as introduced in game theory by Maynard Smith
- is not the only important evolutionary aspect in a evolutionary dynamics,
since complex interdependencies, competition, and growth should be modeled by,
for example, reactive aspects. In the ultimatum game the reciprocity and the
fifty-fifty partition seems to be a deviation from rational behavior of the
players under the light of the Nash equilibrium concept.Such equilibrium
emerges, for example, from the punishment of the responder who generally tends
to refuse unfair proposals. In the iterated version of the game, the proposers
are able to improve their proposals by adding a value thus making fairer
proposals. Such evolutionary aspects are not properly Darwinian-motivated, but
they are endowed with a fundamental aspect: they reflect their actions
according to value of the offers. Recently, a reactive version of the ultimatum
game where acceptance occurs with fixed probability was proposed. In this
paper, we aim at exploring this reactive version of the ultimatum game where
the acceptance by players depends on the offer. In order to do so, we analyze
two situations: (i) mean field and (ii) we consider players inserted within the
networks with arbitrary coordination. We then show that the reactive aspect,
here studied, thus far not analyzed in the evolutionary game theory literature
can unveil an essential feature for the convergence to fifty-fifty split.
Moreover we also analyze populations under four different polices ranging from
a highly conservative to a moderate one, with respect to decision in changing
the proposal based on acceptations. We show that the idea of gaining less more
times added to the reciprocity of the players is highly relevant to the
"healthy" societies population bargaining concept.
