Non-quasi-linear Agents in Quasi-linear Mechanisms
summary
Mechanisms that are truthful for quasi-linear agents remain structured when agents have convex payment disutility: each best response is a uniform scaling best response of true values and pure Nash equilibria exist (with careful tie-breaking). The analysis uses convex cost curves, a value–payment frontier and a slope-based reduction to a quasi-linear instance via fixed-point arguments. For additive valuations and VCG (itemwise second-price), any equilibrium guarantees transferable welfare at least half of optimum.
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