Abstract
In this paper we revisit the rule of k names from a game theoretic perspective. This rule can be described as follows. Given a set of candidates for a position, a committee (formed by the proposers) selects k elements of that set using a screening rule; then a single individual from outside the committee (the chooser) chooses for the position one of the k selected candidates. In this context we first give conditions for the existence of a subgame perfect equilibrium. Then we provide conditions for the existence of subgame perfect q-strong equilibria when the screening rule is \(\pi \)-majoritarian. Finally, we show that when the chooser can strategically appoint a delegate to choose on behalf of him, the conditions for the existence of subgame perfect q-strong equilibria are weaker.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
In fact, the classes we define here are more general because Barberà and Coelho deal with symmetric rules and we do not.
\((\mathbf{x}_M,{{\bar{\mathbf{x}}}}_{N_p\setminus M})\) denotes the vector \(((x_i)_{i\in M}, ({\bar{x}}_j)_{j\in N_p\setminus M})\).
A chooser’s \((|A|-k+1)\)-top candidate is anyone belonging to the set of the \(|A|-k+1\) candidates preferred by the chooser.
We write \(a\succ _i b\) when \(b\not \succeq _i a\) (for any \(a,b\in A\) and any \(i\in N_p\)).
References
Aumann R (1959) Acceptable points in general cooperative n-person games. In: Luce R, Raiffa H (eds) Contributions to the theory of games IV, annals of mathematics studies 40. Princeton University Press, Princeton
Barberà S, Coelho D (2008) How to choose a non-controversial list with \(k\) names. Soc Choice Welf 31:79–96
Barberà S, Coelho D (2010) On the rule of \(k\) names. Games Econ Behav 70:44–61
Barberà S, Coelho D (2017) Balancing the power to appoint officers. Games Econ Behav 101:189–203
Colomer JM (1995) Game theory and the transition to democracy. Edward Elgar, The Spanish Model
Fershtman C, Judd KL, Kalai E (1991) Observable contracts: strategic delegation and cooperation. Int Econ Rev 32:551–559
Pérez J, Jimeno JL, García E (2012) No show paradox in condorcet \(k\)-voting procedures. Group Decis Negot 21:291–303
Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4:25–55
van Damme E, Furth D (2002) Game theory and the market. In: Borm P, Peters H (eds) Chapters in game theory. Kluwer Academic Publishers, Dordrecht
Winter E, Méndez-Naya L, García-Jurado I (2017) Mental equilibrium and strategic emotions. Manag Sci 63:1302–1317
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work has been supported by the ERDF, the MINECO/AEI grantsMTM2014-53395-C3-1-P, MTM2017-87197-C3-1-P, MTM2017-87197-C3-3-P, and by the Xunta de Galicia (Grupo de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01). Authors acknowledge the comments of an anonymous referee.
Rights and permissions
About this article
Cite this article
García-Jurado, I., Méndez-Naya, L. Subgame Perfection and the Rule of k Names. Group Decis Negot 28, 805–825 (2019). https://doi.org/10.1007/s10726-019-09625-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10726-019-09625-6