A Decentralized Mechanism Implementing in Nash Equilibria the Optimal Centralized Solution of a Supply-Chain Problem

44 Pages Posted: 19 Nov 2010

See all articles by Shrutivandana Sharma

Shrutivandana Sharma

Singapore University of Technology and Design (SUTD)

Volodymyr Babich

McDonough School of Business, Georgetown University

Demosthenis Teneketzis

University of Michigan at Ann Arbor - Department of Electrical Engineering and Computer Science

Mark P. Van Oyen

University of Michigan at Ann Arbor

Date Written: November 18, 2010

Abstract

We study the coordination of production decisions for multiple products among many manufacturers and many suppliers, each with private information about its own objective and its own production capabilities. Our methodology does not require a probabilistic model of the beliefs of each decision maker (manufacturer or supplier) regarding asymmetric information. We discover a game form (decentralized mechanism) which implements in Nash Equilibria the solution of the corresponding centralized supply chain problem. In our mechanism the buyers and sellers in the supply chain submit bids/o ers for the quantities they would like to buy/sell and the prices they would like other buyers/sellers to pay/receive per unit of a product. We provide rules for allocating orders and determining payments based on the bids/o ers. We show that, in equilibrium, the unit price for all rms supplying a particular product is equal to the unit price for all rms buying the product. One could interpret this price as the clearing price for the product in the internal market among rms or among divisions of the same rm. Unlike prior work on coordinating rm's production and sales decisions through internal markets, our model does not require a centralized planner to set the prices in the internal markets. Instead, the clearing prices are part of the equilibrium outcome.

Keywords: Supply-chain coordination, asymmetric information, competitive/selfish traders, mechanism design, Nash implementation

Suggested Citation

Sharma, Shrutivandana and Babich, Volodymyr and Teneketzis, Demosthenis and Van Oyen, Mark P., A Decentralized Mechanism Implementing in Nash Equilibria the Optimal Centralized Solution of a Supply-Chain Problem (November 18, 2010). Available at SSRN: https://ssrn.com/abstract=1710733 or http://dx.doi.org/10.2139/ssrn.1710733

Shrutivandana Sharma

Singapore University of Technology and Design (SUTD) ( email )

20 Dover Drive
Singapore, 138682
Singapore

Volodymyr Babich (Contact Author)

McDonough School of Business, Georgetown University ( email )

3700 O Street, NW
Washington, DC 20057
United States

Demosthenis Teneketzis

University of Michigan at Ann Arbor - Department of Electrical Engineering and Computer Science ( email )

1101 Beal Avenue
Ann Arbor, MI 48109
United States

Mark P. Van Oyen

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

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