Summary
This paper deals with a geometrical optimization that is motivated by locational conflicts [cf.Ostmann; Richter, 1978;Rosenmüller, 1979].
Such location conflicts deserve interest in the theory of committee decisions, and more generally in the theory of collective choice, in game theory and the theory of experimental games, but also in public goods theory (cf. references below).
This paper focuses on two solution concepts for locational conflicts which may be attributed toRawls [1971] andKolm [1972].
The analysis of these solutions will make the body of the paper. We shall derive statements concerning continuity and single-valuedness of the “maximizers”.
Problems and results will be illustrated by a detailed discussion of the subset of all locational conflicts involving at most three persons.
This paper heavily relies on the fact that the optimization allows a straight-forward geometric interpretation.
Zusammenfassung
Der folgende Artikel handelt von geometrischer Optimierung. Die Optimierungsaufgaben stammen aus der Behandlung von Standortkonflikten [vgl.Ostmann; Richter, 1978;Rosenmüller, 1979] in verschiedenen theoretischen Rahmen (etwa: Theorien kollektiver Entscheidungen, Spieltheorie, experimentelle Spiele, aber auch: Theorie der öffentlichen Güter, vgl. Literaturhinweise).
Im Mittelpunkt stehen zwei Lösungskonzepte, die aufRawls [1971] undKolm [1972] zurückgehen. Für Standortkonflikte werden die entsprechenden Optimierungsaufgaben aufgestellt und Aussagen über Stetigkeit und Einwertigkeit der Optimierer abgeleitet.
Die zentralen Fragestellungen, Konstruktionen und Ergebnisse werden ausführlicher am Beispiel der 3-Personen-Standortkonflikte studiert.
Wesentlich für die Methodik dieses Artikels ist die Möglichkeit, die Optimierungsaufgaben in kanonischer Weise geometrisch zu interpretieren.
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Ostmann, A. Fair solutions for locational conflicts. Zeitschrift für Operations Research 26, 87–103 (1982). https://doi.org/10.1007/BF01917101
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DOI: https://doi.org/10.1007/BF01917101