Securely implementable social choice functions in divisible and nonexcludable public good economies with quasi‐linear utility functions

• Published date: 01 June 2018
• Author: Katsuhiko Nishizaki
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/jpet.12282

Received: 2 May2016 Accepted: 21 October 2017

DOI: 10.1111/jpet.12282

ARTICLE

Securely implementable social choice functions

in divisible and nonexcludable public good

economies with quasi-linear utility functions

Katsuhiko Nishizaki1,2

1GraduateSchool of Economics, Momoyama

GakuinUniversity

2ResearchInstitute for Socionetwork Strategies,

KansaiUniversity

KatsuhikoNishizaki, Graduate School of Eco-

nomics,Momoyama Gakuin University, 1-1

Manabino,Izumi, Osaka 594-1198, Japan (ka-

nishi@andrew.ac.jp);and Research Institute

forSocionetwork Strategies, Kansai University,

3-3-35,Yamate, Suita, Osaka 564-8680, Japan.

Theauthor wishes to thank the editor, Rabah

Amir,the associated editor,and two anonymous

refereesfor their valuable comments and efforts.

Thispaper is based on Chapter 2 of the author's

PhDthesis submitted to the Graduate School

ofEconomics at Osaka University. The author

isgrateful to TatsuyoshiSaijo, Shigehiro Ser-

izawa,and Yukihiro Nishimura for their helpful

adviceon the thesis. This paper is also a product of

researchthat was financially supported (in part)

bythe Kansai University Subsidy for Supporting

YoungScholars (2014) “Robustness of Secure

Implementation”and a research grant from Kan-

saiUniversity and Matching Fund Subsidy from

MEXT(Ministry of Education, Culture, Sports,

Scienceand Technology) Joint Usage / Research

Centerat the Research Institute for Socionet-

workStrategies, Kansai University (2015–2017)

“ImplementationTheory and Rationality: Secure

ImplementationReconsidered.” Any errors in this

paperare entirely the responsibility of the author.

This paper studies the possibility of secure implementation (Saijo

et al., 2007) in divisible and nonexcludable public good economies

with quasi-linear utility functions. In these economies, although Saijo

et al. (2007) showed that the Grovesmechanisms (Groves, 1973) are

securely implementable when the valuation functions of the pub-

lic good are (i) differentiable, concave, and (ii) identified with a real

number,respectively, this paper shows the following negative result:

securely implementable social choice functions are dictatorial or

constant when the valuation functions of the public good are strictly

increasing and strictly concave.

1INTRODUCTION

This paper considers divisible and nonexcludable public good economies in which n≥2 agents collectively decide (i)

how much of the public good (e.g., seawalls, protection forests, and storm sewers) should be provided and (ii) how

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2017 Wiley Periodicals,Inc. wileyonlinelibrary.com/journal/jpet Journal of Public Economic Theory.2018;20:424–436.