Non-cooperative game theory predicts that Allocators in Ultimatum game
s will take almost all the 'cake'. Experimental evidence is in sharp c
ontrast with this prediction, as several experiments show that the mod
al offer is the even split. interpretations of such results usually ma
ke reference to two competing explanations. One invokes the notion of
fairness; the second argues that in the absence of common knowledge of
the rationality and beliefs of Recipients, Allocators raise their off
ers because they expect that non-satisfactory offers might be rejected
. Although several experiments have been successful in inducing more s
elfish offers by manipulating the Allocators' expectations, they have
done so predominantly by means of extrinsic manipulations that are not
accounted for by game theory. The present study introduces a minor va
riation of the Ultimatum game by implanting a discounting factor, delt
a (0 less than or equal to delta less than or equal to 1), in the stan
dard game, Whereas game theory is indifferent to this modification, ex
perimental results from the modified game show that by continuously ch
anging delta, it is possible to induce systematic changes in Allocator
s' and Recipients' behaviors and beliefs. These results are used to co
mpetitively test the fairness and expectations hypotheses.