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Social choice and game theory: recent results with a topological approach

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  • Chichilnisky, Graciela

Abstract

This chapter presents a summary of recent results obtained in game and social choice theories, and highlights the application and the development of tools in algebraic topology. The purpose is expository: no attempt is made to provide complete proofs, for which references are given, nor to review the previous work in this area, which covers a significant subset of the economic literature. The aim is to provide an oriented guide to recent results, through economic examples with geometric interpretations, and to indicate possible fruitful avenues of research.

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File URL: http://mpra.ub.uni-muenchen.de/8059/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8059.

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Date of creation: 1983
Date of revision:
Handle: RePEc:pra:mprapa:8059

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Related research

Keywords: social choice; game theory; algebraic topology; topological; pareto condition; preferences; Nash equilibrium; transversality;

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References

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  1. Chichilnisky, Graciela & Heal, Geoffrey, 1984. "Patterns of power: bargaining and incentives in two-person games," Journal of Public Economics, Elsevier, vol. 23(3), pages 333-349, April.
  2. Chichilnisky, Graciela, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, MIT Press, vol. 97(2), pages 337-52, May.
  3. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
  4. Brown, Donald J, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, MIT Press, vol. 89(3), pages 456-69, August.
  5. Chichilnisky, G. & Heal, G.M., 1995. "Social Choice with Infinite Populations: Construction of a Rule and Impossibility Results," Papers 95-19, Columbia - Graduate School of Business.
  6. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  8. Chichilnisky, Graciela, 1980. "Continuous representation of preference," MPRA Paper 8042, University Library of Munich, Germany.
  9. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
  10. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March.
  11. Chichilnisky, Graciela, 1977. "Spaces of economic agents," Journal of Economic Theory, Elsevier, vol. 15(1), pages 160-173, June.
  12. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
  13. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
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Citations

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Cited by:
  1. Chichilnisky, Graciela, 1990. "Social choice and the closed convergence topology," MPRA Paper 8353, University Library of Munich, Germany.
  2. Alex Coram, 2006. "Social choice with a continuous ordering function," UMASS Amherst Economics Working Papers 2006-09, University of Massachusetts Amherst, Department of Economics.
  3. Luigi Marengo & Simona Settepanella, 2010. "Social choice among complex objects," LEM Papers Series 2010/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  4. Alex Coram, 2008. "Social choice and information: a note on the calculus of mappings from utility spaces," UMASS Amherst Economics Working Papers 2008-04, University of Massachusetts Amherst, Department of Economics.
  5. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
  6. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer, vol. 33(3), pages 449-476, September.

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