We consider agents with non-linear preferences given by private values and private budgets. We quantify the extent to which posted pricing approximately optimizes welfare and revenue for a single agent. We give a reduction framework that extends the approximation of multi-agent pricing-based mechanisms from linear utility to nonlinear utility. This reduction framework is broadly applicable as Alaei et al. (2012) have shown that mechanisms for linear agents can generally be interpreted as pricing-based mechanisms. We give example applications of the framework to oblivious posted pricing (e.g., Chawla et al., 2010), sequential posted pricing (e.g., Yan, 2011), and virtual surplus maximization (Myerson, 1981).
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