Bertrand-Edgeworth Bidding Game with Asymmetric Suppliers: Theory and Applications

45 Pages Posted: 19 Aug 2010 Last revised: 14 May 2014

See all articles by Shanshan Hu

Shanshan Hu

Indiana University - Kelley School of Business - Department of Operation & Decision Technologies

Roman Kapuscinski

University of Michigan, Stephen M. Ross School of Business

William S. Lovejoy

University of Michigan, Stephen M. Ross School of Business

Date Written: November 15, 2013

Abstract

Motivated by supply competitions in the service sector, we consider a version of the Bertrand-Edgeworth game where capacitated suppliers compete in prices to serve a deterministic demand and a price cap is imposed exogenously. We characterize the equilibrium structure for games with multiple suppliers that are asymmetric in cost and capacity. A pure-strategy equilibrium exists only in special cases, otherwise a mixed-strategy equilibrium prevails. For a mixed-strategy equilibrium, we show there exists an anchoring supplier whose pricing range covers those of the other suppliers, and we pin down the lower and upper bounds of that price range. We derive a canonical closed-form solution for a set of games, and for other more general cases, we demonstrate a numerical scheme for equilibrium calculation. In contrast to a well-known intuition established in the existing literature, we identify a new equilibrium pricing structure in games with N >= 3 suppliers who have similar costs but different capacities: A low-capacity supplier's price distribution is more concentrated than those of its high-capacity competitors, by spanning a smaller interval. We demonstrate an interesting strategy for a buyer with a competitive supply base: Subsidizing a cost-competitive incumbent may reduce the total procurement cost.

Keywords: service procurement; mixed-strategy equilibrium; capacity constraint

JEL Classification: C72, D24, D43, D44

Suggested Citation

Hu, Shanshan and Kapuscinski, Roman and Lovejoy, William S., Bertrand-Edgeworth Bidding Game with Asymmetric Suppliers: Theory and Applications (November 15, 2013). Available at SSRN: https://ssrn.com/abstract=1659996 or http://dx.doi.org/10.2139/ssrn.1659996

Shanshan Hu (Contact Author)

Indiana University - Kelley School of Business - Department of Operation & Decision Technologies ( email )

Business 670
1309 E. Tenth Street
Bloomington, IN 47401
United States
812-856-2342 (Phone)

Roman Kapuscinski

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

William S. Lovejoy

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
113
Abstract Views
916
rank
243,608
PlumX Metrics