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Existence of equilibria in a decentralized two-level supply chain

  • Morales, Dolores Romero
  • Vermeulen, Dries

In 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.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 197 (2009)
Issue (Month): 2 (September)
Pages: 642-658

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Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:642-658
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. 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.
  2. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  3. Adam Brandenburger & Harborne Stuart, 2007. "Biform Games," Management Science, INFORMS, vol. 53(4), pages 537-549, April.
  4. 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.
  5. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, 03.
  6. 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.
  7. McLennan, Andrew, 1989. "Fixed Points of Contractible Valued Correspondences," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 175-84.
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