Finite purchasing power and computations of Bertrand–Nash equilibrium prices

W. Morrow ()

Computational Optimization and Applications, 2015, vol. 62, issue 2, 477-515

Abstract: This article considers the computation of Bertrand–Nash equilibrium prices when the consumer population has finite purchasing power. The literal KKT conditions for equilibria contain “spurious” solutions that are not equilibria but can be computed by existing software, even with prominent regularization strategies for ill-posed problems. We prove a reformulated complementarity problem based on a fixed-point representation of equilibrium prices improves computational reliability and provide computational evidence of its efficiency on an empirically-relevant problem. Scientific inferences from empirical Bertrand competition models with explicit limits on individual purchasing power will benefit significantly from our proposed methods for computing equilibrium prices. An analysis of floating-point computations also implies that any model will have finite purchasing power when implemented on existing computing machines, and thus the techniques discussed here have general value. We discuss a heuristic to identify, and potentially mitigate, the impact of computationally-imposed finite purchasing power on computations of equilibrium prices in any model. Copyright Springer Science+Business Media New York 2015

Keywords: Bertrand–Nash equilibrium prices; Mixed complementarity problems; Ill-posed problems; Finite purchasing power; Mixed logit models (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-015-9743-7 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:62:y:2015:i:2:p:477-515

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9743-7

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().