常数相对风险厌恶多单位拍卖的比较静态与定价结构

The Comparative Static and Pricing Structure of Multi-Unit Discriminatory Auctions with Constant Relative Risk-aversion Bidders

考虑竞价者具有常数相对风险厌恶时的多单位拍卖问题,讨论均衡出价与风险偏好以及价值分布之间的关系.在竞价者具有相同的风险偏好的对称拍卖情形,利用风险中性等价导出了比较静态的充要条件,这一充要条件综合了风险偏好和价值分布的变化.在竞价者具有不同的风险偏好的非对称拍卖中,导出了均衡出价关于风险偏好的线性定价结构,依据这一结构,对任意给定出价,竞价者要求的剩余是其风险厌恶参数的线性函数,并且可以分解为竞争性剩余和风险厌恶剩余.

This paper considered multi-unit discriminatory auctions with constant relative risk-aversion bidders, and explored the special structure of its equilibrium strategy and how the risk preferences of the bidders, also the distributions of bidders value influenced the equilibrium bids. By introducing the concept of risk-neutral equivalent distribution, the case of con- stant relative risk-aversion was transformed into the case of risk neutral. This transformation enables us to combine the influ- ences of the risk preferences and distributions upon the bids to get an equivalent condition for the comparative relation. The sit- uations in which different bidders have different constant relative risk-aversions shows that the equilibrium bids depend linearly on risk reference parameters. Based on this pricing structure, this paper introduced the concepts of ＂demanded surplus＂, ＂competition surplus＂ and ＂risk-aversion surplus＂, and finds that the first one can be decomposed to be the algebraic sum of the lat- ter two.