Dipartimento di Scienze Economiche, Matematiche e Statistiche
Università degli Studi di Foggia
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Some Results on Von Neumann and
Morgenstern’s Stable Set in Multidimentional
Majority rule Games
Francesco Ciardiello, Anindya Bhattacharya
e Victoria Brosi
Quaderno n. 05/2009
“Esemplare fuori commercio per il deposito legale agli effetti della legge 15 aprile 2004 n. 106”
Quaderno riprodotto dal Dipartimento di Scienze Economiche, Matematiche e Statistiche
nel mese di aprile 2009 e depositato ai sensi di legge.
Authors only are responsible for the content of this reprint.
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Dipartimento di Scienze Economiche, Matematiche e Statistiche, Largo Papa Giovanni Paolo II, 1,
71100 Foggia (Italy), Phone +39 0881-75.37.30, Fax +39 0881-77.56.16
Some Results on Von Neumann and Morgenstern’s
Stable Set in Multidimentional Majority Rule Games
1
Francesco Ciardiello 2
Department of Economics, Mathematics, and Statistics,
University of Foggia
Largo Papa Giovanni Paolo II 1 71100 Foggia, Italy.
Tel.: +39 0881753708
Fax: +39 0881753709
[email protected]
Anindya Bhattacharya
Department of Economics and Related Studies,
The University of York
York YO10 5DD, United Kingdom.
Tel.: +44 (0)1904432307
Fax: +44 (0)1904433759
[email protected]
Victoria Brosi
Department of Economics and Related Studies,
The University of York
York YO10 5DD, United Kingdom.
[email protected]
Abstract
In this work we explore some properties of von-Neumann-Morgenstern
stable sets in the environment of multidimensional spatial voting situations. In our framework, the set of outcomes under consideration is some
compact and convex subset of some finite dimensional Euclidean space and
any majority coalition can enforce any outcome from another. Among the
more significant results, we show that contrary to the well-known claim
in Cox, 1987 (repeated in many subsequent works), a stable set in such
an environment does not necessarily coincide with the core even when the
core is non-empty. We also study when such a stable set may be finite.
1 We thank Gary Cox, John Duggan, Roberto Lucchetti and Elizabeth Maggie-Penn for
their help.
Brosi thanks ESRC, UK for a scholarship.
This paper was born when Ciardiello visited the Department of Economics and Related Studies, University of York, UK in 2008. He thanks the department and especially Peter Simmons
for the kind hospitality. He also thanks Luciana Colelli and the Italian institution "Regione
Puglia" for having supported him financially.
The errors and shortcomings remaining are, of course, ours.
2 Corresponding Author.
1