= Revenue-optimal public-project auction
{title2=$x(v)=\mathbf1_{\{\sum_i\phi_i(v_i)\geq0\}}$}
In a public-project <single-parameter mechanism>, all players receive the same binary allocation. For independent <regular priors> and voluntary participation with zero outside utility, maximizing <virtual surplus> means providing the project exactly when $\sum_i\phi_i(v_i)\geq0$. The allocation is monotone in each value, so <critical-value payments> implement it with <dominant-strategy incentive compatibility> and <ex post individual rationality>. For independent uniform values on $[0,1]$, the condition is $\sum_i v_i\geq n/2$, with winning payment $\max\{0,n/2-\sum_{j\ne i}v_j\}$.
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