Existence of equilibria in a decentralized two-level supply chain
AbstractIn this paper, we analyze equilibria in competitive environments under constraints across players' strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani's fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue. Our main motivation to study this problem of co-dependency comes from the field of supply chain planning. A set of buyers is faced with external demand over a planning horizon, and to satisfy this demand they request inputs from a set of suppliers. Both suppliers and buyers face production capacities and they plan their own production in a decentralized manner. A well-known coordination scheme for this setting is the upstream approach where the plan of the buyers is used to decide the request to the suppliers. We show the existence of equilibria for a (shared) inventory cost minimization version of this coordination scheme in which a distribution center manages the inventory of the inputs. However, we illustrate with an example that the centralized solution is not, in general, an equilibrium, suggesting that regulation may be needed.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Maastricht University in its series Open Access publications from Maastricht University with number urn:nbn:nl:ui:27-23092.
Date of creation: 2009
Date of revision:
Publication status: Published in European journal of operational research (2009) v.197, p.642-658
Contact details of provider:
Web page: http://www.maastrichtuniversity.nl/web/Home.htm
Other versions of this item:
- Morales, Dolores Romero & Vermeulen, Dries, 2009. "Existence of equilibria in a decentralized two-level supply chain," European Journal of Operational Research, Elsevier, vol. 197(2), pages 642-658, September.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kohlberg, Elon & Mertens, Jean-Francois, 1986.
"On the Strategic Stability of Equilibria,"
Econometric Society, vol. 54(5), pages 1003-37, September.
- E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
- KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bhatnagar, Rohit & Chandra, Pankaj & Goyal, Suresh K., 1993. "Models for multi-plant coordination," European Journal of Operational Research, Elsevier, vol. 67(2), pages 141-160, June.
- McLennan, Andrew, 1989. "Fixed Points of Contractible Valued Correspondences," International Journal of Game Theory, Springer, vol. 18(2), pages 175-84.
- Dudek, Gregor & Stadtler, Hartmut, 2005. "Negotiation-based collaborative planning between supply chains partners," European Journal of Operational Research, Elsevier, vol. 163(3), pages 668-687, June.
- Alejandro Saporiti & Fernando Tohmé, 2006.
"Single-Crossing, Strategic Voting and the Median Choice Rule,"
Social Choice and Welfare,
Springer, vol. 26(2), pages 363-383, April.
- Alejandro Saporiti & Fernando Tohmé, 2003. "Single-Crossing, Strategic Voting and the Median Choice Rule," CEMA Working Papers: Serie Documentos de Trabajo. 237, Universidad del CEMA.
- Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, 03.
- Adam Brandenburger & Harborne Stuart, 2007. "Biform Games," Management Science, INFORMS, vol. 53(4), pages 537-549, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (J.Odekerken).
If references are entirely missing, you can add them using this form.