  A quantum game can be viewed as a state preparation in which the final output
state results from the competing preferences of the players over the set of
possible output states that can be produced. It is therefore possible to view
state preparation in general as being the output of some appropriately chosen
(notional) quantum game. This reverse engineering approach in which we seek to
construct a suitable notional game that produces some desired output state as
its equilibrium state may lead to different methodologies and insights. With
this goal in mind we examine the notion of preference in quantum games since if
we are interested in the production of a particular equilibrium output state,
it is the competing preferences of the players that determine this equilibrium
state. We show that preferences on output states can be viewed in certain cases
as being induced by measurement with an appropriate set of numerical
weightings, or payoffs, attached to the results of that measurement. In
particular we show that a distance-based preference measure on the output
states is equivalent to a having a strictly-competitive set of payoffs on the
results of some measurement.
