For one scarce facility, the asymptotically optimal truthful mechanism is the quantile that minimizes a Wasserstein-type transport cost; for two facilities, a grid search finds the best equilibrium-stable percentile mechanism.
From our hypothesis, we have thatp2´ p1ą 2 3 thus we either have thatp1ď q1 2 or p2ď 1´ q2 2
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Designing Optimal Mechanisms to Locate Facilities with Insufficient Capacity for Bayesian Agents
For one scarce facility, the asymptotically optimal truthful mechanism is the quantile that minimizes a Wasserstein-type transport cost; for two facilities, a grid search finds the best equilibrium-stable percentile mechanism.