MSMoD43
Stochastic Equilibrium Problems: Economic Modeling, Analysis and Computation
Date: August 10
Time: 13:3015:30
Room: 41
(Note: Click title to show the abstract.)
Organizer:
Su, CheLin (Univ. of Chicago)
Abstract: Motivated by empirical demand estimation problems in economics, the objective of this minisymposium is to discuss and address both theoretical and numerical challenges of stochastic equilibrium problems, arisen from estimation and pricing of pure characteristics demand models. The four presentations aim to first provide an overview of stochastic equilibrium problems and their economic applications, to discuss a regularization method for analyzing and solving stochastic equilibrium problems, to examine the analysis of sample average approximation for a pricing problem formulated as a stochastic equilibrium problem, and finally, to present alternative formulations for studying estimation and pricing problems.
MSMoD431
13:3014:00
Regularized Mathematical Programs with Stochastic Equilibrium Constraints:
Estimating Structural Demand Models
Chen, Xiaojun (Department of Applied Mathematics, The Hong Kong Polytechnic Univ.)
Abstract: The article considers a particular class
of optimization problems involving setvalued stochastic equilibrium constraints.
We develop a solution procedure that relies on an approximation scheme for the equilibrium constraints. Based on regularization, we replaces the approximated equilibrium
constraints by those involving only singlevalued Lipschitz continuous functions. In addition, sampling has the further effect of replacing the
`simplified' equilibrium constraints by more manageable ones obtained by implicitly
discretizing the (given) probability measure so as to render the problem
computationally tractable. Convergence
is obtained by relying, in particular, on the graphical convergence of the
approximated equilibrium constraints. The problem of estimating the
characteristics of a demand model, a widely studied problem in microeconometrics,
serves both as motivation and illustration of the regularization and sampling
procedure.
MSMoD432
14:0014:30
Sample Average Approximation Regularized Method for Products Pricing Problem Based on Pure
Characteristics Demand Models
Hailin, Sun (Nanjing Univ. of Sci. & Tech.)
Chen, Xiaojun (Department of Applied Mathematics, The Hong Kong Polytechnic Univ.)
Su, CheLin (Univ. of Chicago)
Abstract: Utilitybased choice models are often used to determine a consumer's purchase decision among a list of available products. By a pure characteristics model, we consider a firm's multiproduct pricing problem. A sample average approximation (SAA) method is used to approximate the expected market share of products considered and the firm's profit. We then apply a regularized method to compute a solution of the SAA problem and study the convergence of the SAA solutions.
MSMoD433
14:3015:00
Topics in Computing Nash Equilibria
Pang, JongShi (Univ. of Southern California)
Abstract: This talk presents results on two topics pertaining to the computation of Nash equilibria in noncooperative games. These are: (a) equilibrium constrained optimization, and (b) games with minmax players. The former topic is treated more broadly under the framework of variationalinequality constrained hemivariational inequality. Interestingly, a particular pullout approach for solving the latter class of games can be applied to a sampled version of games with stochastic recourse functions.
MSMoD434
15:0015:30
A Constructive Approach to Estimating Pure Characteristics Demand Models with
Pricing
Su, CheLin (Univ. of Chicago)
Pang, JongShi (Univ. of Southern California)
Abstract: We consider estimating pure characteristics demand models. The main difficulty in solving this problem is that market share equations are nonsmooth. To overcome this difficulty, we first characterize consumers' purchase decisions by a system of complementarity constraints. This new characterization leads to smooth approximated market share equations and allows us to cast the estimation problem as a mathematical program with complementarity constraints. We present numerical results to demonstrate the computational effectiveness of our approach.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
