  We consider a repeated game where a player self-reports her usage of a
service and is charged a payment accordingly by a center. The center observes a
partial signal, representing part of the player's true consumption, which is
generated from a publicly known distribution. The player can report any value
that does not contradict the signal and the center issues a payment based on
the reported information. Such problems find application in net metering
billing in the electricity market, where a customer's actual consumption of the
electricity network is masked and complete verification is impractical. When
the underlying true value is relatively constant, we propose a penalty
mechanism that elicits truthful self-reports. Namely, besides charging the
player the reported value, the mechanism charges a penalty proportional to her
inconsistent reports. We show how fear of the uncertainty in the future
incentivizes the player to be truthful today. For Bernoulli distributions, we
give the complete analysis and optimal strategies given any penalty. Since
complete truthfulness is not possible for continuous distributions, we give
approximate truthful results by a reduction from Bernoulli distributions. We
also extend our mechanism to a multi-player cost sharing setting and give
equilibrium results.
