According to Duranton (2008), the main focus of spatial economics is the location choice of the economic agents. In order to explain the location and the agglomeration of agents in certain locations, one must relax the core assumptions of the neoclassic competitive framework. According to Fujita and Thisse (2002), three alternatives emerged and had huge attention in the literature: the assumption of heterogeneity of locations, as in comparative advantage models or in pioneering static location models; the externality models, in which economic activity endogenously generates spillovers that motivates the agglomeration of the agents; the assumption of imperfect markets, implying that the agents have to interact with each other, as in spatial competition models or in the monopolistic competition approach. This review will focus on the development of spatial competition models. Specifically, the main purpose is to study models in which the location choice by firms plays a major role. Therefore, after a brief review of the roots of spatial competition models, this paper intends to offer a critical analysis over the recent developments in spatial competition modeling. The starting point is the recognition of the increased importance of this topic through the quantification of the research in this field by using bibliometric tools. After that, this study proceeds by identifying the main research paths within spatial competition modeling. Specifically, the type of strategie (Bertrand vs. Cournot competition) and its implications over location equilibria are discussed. Additionally, it is presented a comparison of the impact of the most studied assumptions in literature, that respect to the market (linear vs. circular), production costs, transportation costs, as well as the number of firms. Finally, the type of information (complete vs. incomplete) and its effects over the equilibria are also discussed.
