Consider a community with $n$ residents. The undertaking of a public project with a given cost $C > 0$ is being considered.
Each resident $i$ is simultaneously asked to report his utility $r_i$ in case the public project is undertaken. If the sum of reported utilities $r_1+r_2+\ldots +{r}_n \ge C$, then the public project is implemented; otherwise it is shelved away.
If $r_1+r_2+\ldots +{r}_n \ge C$, then each resident $i$ is asked to pay an amount $p_i$ which is a known function of the vector of reported utilities. Thus, if $u_i$ is $i$'s true utility, his payoff is $$u_i - p_i (r_1, \ldots, r_n)$$ if the project is implemented, and it is $0$ otherwise.
How can determine the prices in order to guarantee a truthful mechanism? In other words, is it possible to find a vector of price functions ${p}_1,{p}_2...{p}_n$ such that all residents sincerely report $r_i = u_i$, instead of giving a deceptive report $r_i \ne {u}_i$?
This is a classic example known in the literature as the Groves-Clarke mechanism for the provision of a public good.
Assuming quasi-linear preferences, this mechanism achieves the efficient allocation and truth-telling is the (equilibrium) dominant strategy. However, the mechanism is not budget-balanced; i.e., it may not raise enough money to cover for the cost of the public project.
A result in the literature shows that it is not possible to simultaneously satisfy these three requirements: 1) truthful implementation in dominant strategies; 2) efficient provision; and 3) budget-balance.