The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.
翻译:然而,对于满足自然正常财产的线性公用事业代理,Alaei等人(2018年)表明,仅贴出匿名价格是一种电子通行。我们给出了非线性公用事业代理的常规性财产参数,并表明对正规代理的匿名定价近似范围大约扩大到满足这种近似正常财产的代理。我们采用这一近似框架来证明匿名定价是相对于公共预算公用事业、私营预算公用事业和(一个特别的)风险反用途的代理商的收益最佳单项拍卖的固定性价格。