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Dominant-strategy incentive compatibility means truthful reporting maximizes a player's utility for every fixed profile of the other reports. It is the monetary-mechanism version of strategyproofness and implies Bayesian incentive compatibility under any independent prior.

Use the usual independent private values model, quasilinear utility, and voluntary participation with zero outside utility. These assumptions matter: without individual rationality, arbitrary type-independent entry charges make revenue unbounded, and correlated types cannot in general be described by their marginal priors alone.

The revelation principle lets us optimize over direct revelation mechanisms satisfying Bayesian incentive compatibility. Write $x(v)\in [0,1]$ for the common project allocation, $X_i(t)={\mathbb{E}}_{V_{-i}}x(t,V_{-i})$ for player $i$'s interim allocation, and $P_i(t)$ for its interim payment. The interim payment identity givesSince interim individual rationality requires $U_i({\underline{v}}_i)\ge 0$, the virtual-surplus revenue identity bounds expected revenue byThe best feasible common allocation at each valuation profile therefore provides the project when total virtual surplus is nonnegative:Because each regular prior has a nondecreasing virtual valuation, this allocation is a nondecreasing function of each player's report. Hold $v_{-i}$ fixed and charge the critical-value paymentThis is the winning threshold when it lies in the support, the lowest allowed value if every type wins, and zero if the player loses. A truthful winner never pays more than its value; a losing type cannot profit by crossing the threshold. Thus the mechanism has dominant-strategy incentive compatibility and ex post individual rationality, with zero utility at every lowest type. It attains the revenue bound, proving optimality even among mechanisms requiring only Bayesian incentive compatibility. At a zero-virtual-surplus tie, choose any fixed rule that preserves monotonicity.

For independent uniform distributions on $[0,1]$, the virtual valuations are ${\varphi }_i(v_i)=2v_i-1$. The revenue-optimal public-project auction becomesWhen it is provided, player $i$ paysotherwise every payment is zero. If the displayed threshold exceeds one, player $i$ cannot induce provision within its allowed support; if it is negative, provision is independent of its own report and its payment is zero. For $n=1$, this specializes to a reserve value and payment of $1/2$.

An equilibrium outcome of a mechanism can be reproduced by asking for types and then sending the messages prescribed by the original equilibrium strategies. Truthful reports are then a Bayesian Nash equilibrium: a profitable false report would induce a profitable original deviation. This reduces optimization over indirect mechanisms to direct revelation mechanisms with Bayesian incentive compatibility, under the same information and participation assumptions.