Chichilnisky, Graciela (1983): Social choice and game theory: recent results with a topological approach. Published in: Social Choice and Welfare , Vol. Chap., (1983): pp. 79-102.
Download (3MB) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Social choice and game theory: recent results with a topological approach|
|Keywords:||social choice; game theory; algebraic topology; topological; pareto condition; preferences; Nash equilibrium; transversality|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory
|Depositing User:||Graciela Chichilnisky|
|Date Deposited:||03. Apr 2008 04:37|
|Last Modified:||16. Mar 2015 11:07|
ARROW, K. J. (1951) Social choice and individual values (Yale Univ. Press).
BLACK, D. (1948) "On the ratioanle of preferences and equilibria", Projectfor Efficiency of Decision Making in Economic Systems, Harvard Universiy.
BROWN, D. (1976) "Aggregation of preferences", Quarterly Journal of Economics.
G. CHICHILNISKY, "Manifolds of preferences and equilibria," Technical Report No. 29, Project on Efficiency of Decision Making in Economic Systems, Harvard Univ, 1976.
CHICHILNISKY, G., (1977), "Spaces of Economic Agents", Journal of Economic Theory, 16 (1), 160-173.
Chichilnisky, G . (1979a) "A General Result on Strong Manipulability", The Economic Workshop, Columbia University .
Chichilnisky, G . (1979b) "On Fixed Points and Social Choice Paradoxes", Economic Letters .
Chichilnisky, G . (1980a) "Continuous Representation of Preferences", Review of Economic Studies .
Chichilnisky, G . (1980b) "Intensity of Preferences and von Neuman Morgenstern Utilities", Working Paper, University of Essex .
Chichilnisky, G . (1980c) "Single Peakedness and the Contractibility of Preference Spaces", Working Paper, University of Essex .
Chichilnisky, G . (1980d) "Social Choice and the Topology of Spaces of Preferences", Advances in Mathematics .
Chichilnisky, G . (1981) "The Structural Instability of Decisive Majority Rules", Journal of Mathematical Economics .
Chichilnisky, G . (1982a) "Social Aggregation Rules and Continuity", Quarterly Journal of Economics .
Chichilnisky, G . (1982b) "The Topological Equivalence of the Pareto Condition and the Existence of a Dictator", Journal of Mathematical Economics .
Chichilnisky, G . (1982c) "Incentive Compatible Games : A Characterization of Strategy and Outcome Spaces", Working Paper No . 139, Columbia University .
Chichilnisky, G . and G . Heal (1979a) "Necessary and Sufficient Conditions for a Resolution of the Social Choice Paradox", Journal of Economic Theory, in press .
Chichilnisky, G . and G . Heal (1979b) "Social Choice with Infinite Population : Construction of a Rule and Impossibility Results", The Economic Workshop, Columbia University .
Chichilnisky, G . and G . Heal (1980) "Patterns of Power : Bargaining and Implementation in two person games", Discussion Paper, University of Essex .
Chichilnisky, G . and G . Heal (1981) "Incentive Compatibility and Local Simplicity", Working Paper, University of Essex .
Chichilnisky, G . and G . Heal (1982) "A Necessary and Sufficient Condition for Straight Forward Games", Working Paper No . 138, Columbia University .
Debreu, G . (1972) "Regular Economies", Econometrica .
Gibbard, A . (1973) "Manipulation of Voting Schemes : A General Result", Econometrica .
Kuiper, N .H . (1971) Varietes Hilbertiennes . Aspects Geometriques, Seminaire de mathematiques Superieures (la Presse de 1'Universite de Montreal) .
Satterthwaite, M .A . (1975) "Strategy-Proofness and Arrow's Conditions : Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions", Journal of Economic Theory .
Sen, A .K . (1970) Collective Choice and Social Welfare (Holden-Day, San Francisco) .
Spanier, E . (1966) Algebraic Topology (McGraw-Hill, New York) .
Vickrey, W . (1960) "Utility, Strategy and Social Decision Rules", Quarterly Journal of Economics .