Ann Reg Sci 2000) 34:451±468 9 999 2000 Network competition and branch di¨erentiation with consumer heterogeneity Jean-Claude Thill Department of Geography, State University of New York at Bu¨alo, 117 Wilkeson Quad, Amherst NY 14261-0023, USA e-mail: jcthill@acsu.bu¨alo.edu) Received: October 1998 / Accepted: June 1999 Abstract. The paper provides a general framework for the analysis of non- cooperative competition between multi-branch networks when consumers have heterogeneous preferences. This framework allows for ill-studied con- ditions, such as branch loyalty and economies of scope, to be explored in terms of their role in shaping address solutions and ®rm pro®ts. Geographic and quality di¨erentiation as well as ®rm pro®ts are shown to be dependent upon the magnitude of the loyalty factor and upon the extend of economies of scope. Real world situations in the retail industry are interpreted in the light of the results of the analysis. 1. Introduction In his 1929 seminal piece, Hotelling set an important benchmark against which several generations of location theorists measured their contribution. The ``Principle of Minimum Di¨erentiation'' is not the unassailable rock it once was. In fact the literature abounds with instances where inter-®rm com- petition is found not to lead to the co-location of ®rms at the center of the market. Reviews of this literature can be found in Jaskold Gabszewicz and Thisse 1986, 1992, and Beckmann and Thisse 1986) In that respect, competi- tion between organizations i.e., multi-branch ®rms, outlet chains or networks) is intriguing because, in Ghosh and McLa¨erty's 1987) words, it involves ``considerations of the system-wide store-location interactions'' p. 127), thus adding at least one degree of complexity to the problem. Teitz 1968) was ®rst to pay serious attention to system-wide competition. Interestingly, he dis- covered that, in some games, solutions were identical to those derived with fully independent outlets, but radically di¨erent in other games. In Thill 1992a), I examine horizontal di¨erentiation of branches serving a market characterized by a geographic dimension and a dimension capturing the overall quality of the shopping experience ambiance, merchandise quality and variety, level of service) ± the quality dimension. Di¨erentiation between branches is inversely related to consumers' willingness to shop at branches distant from their ideal point reservation disutility), and directly related to