Nonlinear Pricing with Random Participation
在代理人外部选择随机化的假设下，重新审视非线性定价中的经典结论，发现垄断者“顶部无扭曲”结论依然成立但底部可能无扭曲或出现捆绑，而双寡头竞争在对称边际成本且竞争激烈时会出现高效质量分配和成本加成定价。
The canonical selection contracting programme takes the agent's participation decision as deterministic and finds the optimal contract, typically satisfying this constraint for the worst type. Upon weakening this assumption of known reservation values by introducing independent randomness into the agents' outside options, we find that some of the received wisdom from mechanism design and nonlinear pricing is not robust and the richer model which allows for stochastic participation affords a more general empirical specification. We develop a multidimensional methodology for addressing this class of problems, providing two important applications to nonlinear pricing. First, with nonlinear pricing by a monopolist the familiar “nodistortion-at-the-top” result persists, but in tandem with the surprising conclusion that there is either no distortion at the bottom or bunching. Second, in a simple model of product differentiated duopolists competing with nonlinear pricing we show that, generally, the duopoly outcome is qualitatively similar to the monopoly outcome. However, when marginal costs are symmetric and competition is sufficiently intense, distortions disappear and the equilibrium outcome takes a remarkably simple form: efficient quality allocations with cost-plus-fee pricing. Copyright 2002, Wiley-Blackwell.