Eliciting Truthful Reports with Partial Signals in Repeated Games

TL;DR

This paper introduces a penalty-based mechanism in repeated games that encourages truthful self-reporting of partial signals about consumption, with applications in electricity billing, and analyzes its effectiveness for Bernoulli and continuous distributions.

Contribution

It proposes a novel penalty mechanism for truthful reporting in repeated settings and provides complete analysis for Bernoulli distributions and approximate results for continuous ones.

Findings

The mechanism incentivizes truthful reporting when true consumption is stable.

Optimal strategies are characterized for Bernoulli distributions.

The approach extends to multi-player cost sharing scenarios.

Abstract

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.