Rationalizable behavior in the Hotelling–Downs model of spatial competition

Joep Sloun ()
Additional contact information
Joep Sloun: Maastricht University

Theory and Decision, 2023, vol. 95, issue 2, No 6, 309-335

Abstract: Abstract We consider two scenarios of the Hotelling–Downs model of spatial competition. This setting has typically been explored using pure Nash equilibrium, but this paper uses point rationalizability (Bernheim, Econometrica J Economet Soc 52(4):1007–1028, 1984) instead. Pure Nash equilibrium imposes a correct beliefs assumption, which may rule out perfectly reasonable choices in a game. Point rationalizability does not have this correct beliefs assumption, which makes this solution concept more natural and permissive. The first scenario is the original Hotelling–Downs model with an arbitrary number of agents. Eaton and Lipsey (Rev Econ Stud 42(1):27–49, 1975) used pure Nash equilibrium as their solution concept for this setting. They showed that with three agents, there does not exist a pure Nash equilibrium. We characterize the set of point rationalizable choices for any number of agents and show that as the number of agents increases, the set of point rationalizable choices increases as well. In the second scenario, agents have limited attraction intervals (Feldman et al. Variations on the Hotelling–Downs model. In: Thirtieth AAAI Conference on Artificial Intelligence, pp 496–501, 2016). We show that the set of point rationalizable choices does not depend on the number of agents, apart from this number being odd or even. Furthermore, the set of point rationalizable choices shrinks as the attraction interval increases.

Keywords: Hotelling–Downs model; Rationalizability; Spatial competition; Product differentiation; Static games (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11238-022-09922-8 Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:theord:v:95:y:2023:i:2:d:10.1007_s11238-022-09922-8

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/11238/PS2

DOI: 10.1007/s11238-022-09922-8

Access Statistics for this article

Theory and Decision is currently edited by Mohammed Abdellaoui

More articles in Theory and Decision from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().