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Comparative statics in stochastic problems with applications.

机译：应用中的随机问题中的比较静力学。

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摘要

This dissertation studies conditions under which optimal solutions to stochastic optimization problems--problems of the form {dollar}maxlimitssb{lcub}rm x,theta{rcub}V({lcub}bf x{rcub},{lcub}bftheta{rcub},{lcub}bf t{rcub},{lcub}bf tau{rcub})equiv intpi{dollar}(x,s;t)dF(s;{dollar}theta,tau{dollar})--are monotone nondecreasing in exogenous parameters. We characterize properties of stochastic objective functions based on properties of the payoff function ({dollar}pi{dollar}) and the probability distribution (F).; In Chapter 1, we focus on problems of the form {dollar}V({lcub}bf theta{rcub};{lcub}bf tau{rcub})equiv intpi{dollar}(s)dF(s;{dollar}{lcub}bf theta{rcub},{lcub}bf tau{rcub}{dollar}) (where all of the variables are vectors). We first develop a result which unifies and extends the existing stochastic dominance literature, proving a class of theorems about monotonicity of V({dollar}{lcub}bf theta{rcub};{lcub}bf tau{rcub}{dollar}). We then show that the method which is used to prove stochastic dominance theorems is exactly the right method for characterizing when V({dollar}{lcub}bf theta{rcub};{lcub}bf tau{rcub}{dollar}) satisfies any property in a class which we call "linear difference properties," a class which includes the properties supermodular and concave. The results about supermodularity of the stochastic objective function can be applied to derive monotone comparative statics predictions.; Chapter 2 studies a second class of optimization problems, which can be written {dollar}intsb{lcub}s{rcub}pi(x,s)dF(s,theta{dollar}), where all variables are real numbers. We characterize Milgrom and Shannon's single crossing property, providing necessary and sufficient conditions so that the optimal x is nondecreasing in {dollar}theta{dollar}. We find that single crossing of the payoff function {dollar}pi{dollar} and the Monotone Likelihood Ratio Order (MLR) on the distribution F together are sufficient for the conclusion--single crossing of the expectation--and further, neither one of the hypotheses can be weakened without strengthening the other. We also prove an analogous result about the Spence-Mirrlees single crossing condition for problems of the form {dollar}intsb{lcub}s{rcub}nu(x,y,s)dF(s,theta{dollar}). The results are applied to signaling games, auction games, and mechanism design.; Chapter 3 applies the results of Chapter 1 to a firm's long-run choices of organization and technology, choices which affect the firm's short-run innovative activity. We focus on flexibility, which affects the future costs of implementing innovations, and information gathering, which affects the future opportunities for innovation. We consider two dimensions of innovation: demand-enhancing (product) and cost-reducing (process). Our analysis reveals that short-run complementarities between these two types of innovation lead to complementarities between its long-run decisions about product and process flexibility and information gathering.
机译：本论文研究了随机优化问题的最优解的条件-形​​式为{dollar} maxlimitssb {lcub} rm x，theta {rcub} V（{lcub} bf x {rcub}，{lcub} bftheta {rcub} ，{lcub} bf t {rcub}，{lcub} bf tau {rcub}）等价intpi {dollar}（x，s; t）dF（s; {dollar} theta，tau {dollar}）-单调非递减在外生参数中。我们基于收益函数（{pilar} pi {dollar}）的属性和概率分布（F）来表征随机目标函数的属性。在第1章中，我们重点讨论{dollar} V（{lcub} bf theta {rcub}; {lcub} bf tau {rcub}）等于intpi {dollar}（s）dF（s; {dollar} { lcub} bf theta {rcub}，{lcub} bf tau {rcub} {dollar}）（其中所有变量都是向量）。我们首先得出一个结果，该结果统一并扩展了现有的随机优势文献，证明了有关V（{dollar} {lcub} bf theta {rcub}; {lcub} bf tau {rcub} {dollar}）单调性的一类定理。然后，我们证明，用于证明随机优势定理的方法恰好是表征V（{dollar} {lcub} bf theta {rcub}; {lcub} bf tau {rcub} {dollar}）满足以下条件时正确的方法类，我们称之为“线性差属性”，该类包括超模和凹的属性。随机目标函数超模态的结果可用于推导单调比较静力学预测。第2章研究了第二类优化问题，可以写成{dollar} intsb {lcub} s {rcub} pi（x，s）dF（s，theta {dollar}），其中所有变量都是实数。我们描述了米尔格罗姆和香农的单一穿越性质，提供了必要和充分的条件，以使最优x在{dollar} theta {dollar}中不变。我们发现，收益函数{dol} pi {dollar}和单调似然比阶数（MLR）在分布F上的单交叉就足以得出结论-期望的单交叉-而且，假说可以在不加强另一个假设的情况下被削弱。对于形式为{dollar} intsb {lcub} s {rcub} nu（x，y，s）dF（s，theta {dollar}）的问题，我们还证明了Spence-Mirrlees单交叉条件的类似结果。结果将应用于信号游戏，拍卖游戏和机制设计。第3章将第1章的结果应用于企业的组织和技术的长期选择，这些选择会影响企业的短期创新活动。我们专注于灵活性，信息灵活性会影响实施创新的未来成本，而信息收集会影响未来的创新机会。我们考虑创新的两个方面：提高需求（产品）和降低成本（过程）。我们的分析表明，这两类创新之间的短期互补会导致其关于产品和流程灵活性以及信息收集的长期决策之间的互补。

著录项

  • 作者

    Athey, Susan Carleton.;

  • 作者单位

    Stanford University.;

  • 授予单位 Stanford University.;
  • 学科 Economics Theory.
  • 学位 Ph.D.
  • 年度 1995
  • 页码 110 p.
  • 总页数 110
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 经济学;
  • 关键词

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