  We study information elicitation in cost-function-based combinatorial
prediction markets when the market maker's utility for information decreases
over time. In the sudden revelation setting, it is known that some piece of
information will be revealed to traders, and the market maker wishes to prevent
guaranteed profits for trading on the sure information. In the gradual decrease
setting, the market maker's utility for (partial) information decreases
continuously over time. We design adaptive cost functions for both settings
which: (1) preserve the information previously gathered in the market; (2)
eliminate (or diminish) rewards to traders for the publicly revealed
information; (3) leave the reward structure unaffected for other information;
and (4) maintain the market maker's worst-case loss. Our constructions utilize
mixed Bregman divergence, which matches our notion of utility for information.
