The single crossing conditions for incomplete preferences

Nikolai Kukushkin ()

International Journal of Game Theory, 2015, vol. 44, issue 1, 225-251

Abstract: We study the implications of the single crossing conditions for preferences described by binary relations. All restrictions imposed on the preferences are satisfied in the case of approximate optimization of a bounded-above utility function. In the context of the choice of a single agent, the transitivity of strict preferences ensures that the best response correspondence is increasing in the sense of a natural preorder; if the preferences are represented by an interval order, there is an increasing selection from the best response correspondence. In a strategic game, a Nash equilibrium exists and can be reached from any strategy profile after a finite number of best response improvements if all strategy sets are chains, the single crossing conditions hold w.r.t. pairs (one player’s strategy, a profile of other players’ strategies), and the strict preference relations are transitive. If, additionally, there are just two players, every best response improvement path reaches a Nash equilibrium after a finite number of steps. If each player is only affected by a linear combination of the strategies of others, the single crossing conditions hold w.r.t. pairs (one player’s strategy, an aggregate of the strategies of others), and the preference relations are interval orders, then a Nash equilibrium exists and can be reached from any strategy profile with a finite best response path. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Strong acyclicity; Single crossing; Cournot tatonnement; Nash equilibrium; Aggregative game (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s00182-014-0427-9 (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:spr:jogath:v:44:y:2015:i:1:p:225-251

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-014-0427-9

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().