Capacity Allocation with Traditional and Internet Channels* Yue Dai, 1 Xiuli Chao, 2 Shu-Cherng Fang, 2,3 Henry L.W. Nuttle 2 1 School of Management, Fudan University, Shanghai 200433, China 2 Industrial Engineering and Operations Research, North Carolina State University, Raleigh, North Carolina, 27695-7906 3 Mathematical Sciences and Industrial Engineering, Tsinghua University, Beijing, China Received 1 May 2006; accepted 1 May 2006 DOI 10.1002/nav.20168 Published online 14 July 2006 in Wiley InterScience (www.interscience.wiley.com). Abstract: In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm’s allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single-product single-period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi-period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics 53: 772–787, 2006 Keywords: capacity allocation; game theory; nash equilibrium; sequential game 1. INTRODUCTION The Internet, as a relatively inexpensive electronic medium, dramatically reduces the transaction costs and increases information availability. By utilizing the Internet, in-stock items can be made available to more customers, and orders can be placed in real time. Internet-based electronic marketplaces have become an integral part of the modern economy. In this study, we consider two competitive firms, each of which has a local store and an online store, namely, its web page. Customers can either visit the local store or order from the web page. We assume that the local store and the online store hold separate stocks. When a stockout occurs at a local store customers may go to the online store belonging to the same firm or visit the local store of the other firm. How- ever, as commonly observed, when a stockout occurs at an online store, customers usually will not visit the local store Correspondence to: Yue Dai (yuedai@fudan.edu.cn) * This work was partially supported by the National Textile Cen- ter of the U.S. Department of Commerce under Grant I01-S01. The first author is supported in part by Chinese NSF under 70502009. The second author is supported in part by NSF under DMI-0196084 and DMI-0200306. belonging to the same firm, but they may go to the online store of the other firm. One question facing each firm is how to allocate its finite capacity (stock) between its local and online stores to maximize its profit as a whole. Because customers may shift from one firm to another when stockout occurs, the capacity allocation of one firm affects the decision of its rival, thereby creating a strategic interaction. Therefore, in this paper game theory is used for the analysis. We first consider a single-product single-period model and assume that the capacity of each firm is given and known. We study two scenarios of this capacity allocation game. Remember that when a stockout occurs at a local store customers may go to the rival’s local store or go to the online store belonging to the same firm. In Scenario 1, it is assumed that those customers who have visited both the local and the online stores of the same firm will leave the system. In Sce- nario 2, we assume that these customers with demand unmet by one firm may go to the rival’s online store before leaving the system. For both scenarios, we present some existence and stability conditions for a Nash equilibrium and conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We further extend the existence result of a Nash equilibrium to a generalized model with © 2006 Wiley Periodicals, Inc.