Abstract
A social choice correspondence is self-implementable in strong equilibrium if it is implementable in strong equilibrium by a social choice function selecting from the correspondence itself as a game form. We characterize all social choice correspondences implementable this way by an anonymous social choice function satisfying no veto power, given that the number of agents is large relative to the number of alternatives. It turns out that these are exactly the social choice correspondences resulting from feasible elimination procedures as introduced in Peleg (Econometrica 46:153–161, 1978).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Here, σ N∖S denotes the restriction of σ to N ∖ S. Similar notation will be used throughout the paper.
- 2.
Dependence on β is often not mentioned when confusion is unlikely.
- 3.
- 4.
- 5.
\(R^i_{|B}\) denotes the restriction of R i to B.
- 6.
- 7.
These functions have been first formally introduced in Moulin and Peleg (1982). Here we just use some of the associated terminology.
- 8.
- 9.
- 10.
Cf. Moulin (1983).
References
Aumann, R. J. (1959) Acceptable points in general cooperative n-person games. In Contributions to the theory of games. Annals of mathematic studies no. 40 (Vol. IV). Princeton, NJ: Princeton University Press.
Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41, 587–602.
Holzman, R. (1986). On strong representations of games by social choice functions. Journal of Mathematical Economics, 15, 39–57.
Hurwicz, L. (1972). On informationally decentralized systems. In C. B. Mcguire & R. Radner (Eds.), Decision and organization. Amsterdam: North-Holland.
Jackson, M. O. (2001). A crash course in implementation theory. Social Choice and Welfare, 18, 655–708.
Maskin, E. (1999). Nash equilibrium and welfare optimality. The Review of Economic Studies, 66, 23–38.
Moulin, H. (1983). The strategy of social choice. Amsterdam: North-Holland.
Moulin, H., & Peleg, B. (1982). Cores of effectivity functions and implementation theory. Journal of Mathematical Economics, 10, 115–145.
Peleg, B. (1978). Consistent voting systems. Econometrica, 46, 153–161.
Peleg, B. (1984). Game theoretic analysis of voting in committees. Cambridge: Cambridge University Press.
Peleg, B., & Peters, H. (2010). Strategic social choice: Stable representations of constitutions. Heidelberg: Springer.
Peleg, B., & Peters, H. (2017a). Feasible elimination procedures in social choice: An axiomatic characterization. Research in Economics, 71, 43–50.
Peleg, B., & Peters, H. (2017b). Choosing k from m: Feasible elimination procedures revisited. Games and Economic Behavior, 103, 254–261.
Polishchuk, I. (1978). Monotonicity and uniqueness of consistent voting systems. Center for Research in Mathematical Economics and Game Theory, Hebrew University of Jerusalem.
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, 10, 187–207.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Peleg, B., Peters, H. (2019). Self-implementation of Social Choice Correspondences in Strong Equilibrium. In: Trockel, W. (eds) Social Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-319-93809-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-93809-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93808-0
Online ISBN: 978-3-319-93809-7
eBook Packages: Economics and FinanceEconomics and Finance (R0)