Location Games
Location games offer simple and parsimonious frameworks for analyzing a host of issues from political competition to product positioning and business strategy. In this chapter, we review existing approaches to modeling spatial competition using location g
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5.1
Introduction
Many problems of pertinent interest to economists, social scientists, political scientists, business strategists, and citizens with an interest in politics are suitably modeled as location games. Examples range from the provision of artwork including songs and movies; the production of articles; and, prior to that, the choice of research agendas to the programming choice of free-to-air radio and TV stations; drug development by pharmaceutical companies; the physical location of (chain) stores; the strategic choices of business managers regarding which territories and
I want to thank the editor, Stefano Colombo, for his patience and persistence, and Bing Liu and Laure Pavaday for their outstanding research assistance. Financial support from the Samuel and June Hordern Endowment is also gratefully acknowledged.
S. Loertscher () Department of Economics, University of Melbourne, Melbourne, VIC, Australia e-mail: [email protected] © The Author(s) 2020 S. Colombo (ed.), Spatial Economics Volume I, https://doi.org/10.1007/978-3-030-40098-9_5
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business strands to be active in; and the choice of policy platforms by political parties or candidates. In a location game, the set of actions available to strategic players is a point in a given space. For the purpose of this chapter, we take this space to be the unit interval, and we assume that there is a continuum of customers (buyers, voters) distributed continuously along that interval. This distribution of customers is captured by a cumulative distribution function F with density f. Customers have bliss point locations, and cater to the player whose location is closest to their bliss point. The payoff of a player is monotonically increasing in the mass of customers it attracts. Often, this payoff is assumed to be linear but, as we shall see, this assumption can typically be relaxed considerably by simply assuming that it is increasing. (Of course, the assumption of linearity is, for example, appropriate for broadcasters, newspapers, online portals, and YouTubers whose net profits are in proportion to the size of their audiences.) To date, location games come in one of two forms. In a simultaneous location game, a given set of firms choose their locations simultaneously, and all firms enter. In contrast, in a sequential location game, a given (large) set of firms can enter and choose locations sequentially at some fixed cost. In any (subgame perfect) equilibrium, only a subset of these firms enter. Location games provide simple, parsimonious, and elegant frameworks that allow one to think about a host of interesting issues in a concise way. Last but not least, location games are fun to think about and great tools for teaching basic game theory. (Un)fortunately, location games are surprisingly robust in some important aspects and terribly fragile in others. In this chapter, we review both robustness and fragility, and lack of tractability of simultaneous and sequential location games, and we discuss a new approach that may com
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