Existence, Uniqueness, and Algorithm for Identifying Free Riders in Multiple Public Good Games: Replacement Function Approach

33 Pages Posted: 21 Jul 2018

See all articles by Ken-ichi Suzuki

Ken-ichi Suzuki

Tohoku University

Jun-ichi Itaya

Hokkaido University - Division of Modern Economics and Management

Akitomo Yamanashi

Hokkaido University

Tatsuyoshi Miyakoshi

Osaka University

Date Written: June 01, 2018

Abstract

This study shows the uniqueness of Nash equilibrium in the model of multiple voluntarily supplied public goods with potential contributors possessing different Cobb-Douglas preferences. This study provides a sufficient condition for uniqueness using graph theory. This sufficient condition allows us to use the replacement function approach of Cornes and Hartley (2007) not only to develop an algorithm for identifying free riders, but also to provide an alternative proof for the uniqueness of a Nash equilibrium in multiple public goods models.

Keywords: public good, voluntary provision, uniqueness, aggregate game, Nash equilibrium, algorithm

JEL Classification: H410, F130, D010

Suggested Citation

Suzuki, Ken-ichi and Itaya, Jun-ichi and Yamanashi, Akitomo and Miyakoshi, Tatsuyoshi, Existence, Uniqueness, and Algorithm for Identifying Free Riders in Multiple Public Good Games: Replacement Function Approach (June 01, 2018). CESifo Working Paper Series No. 7062. Available at SSRN: https://ssrn.com/abstract=3211148

Ken-ichi Suzuki (Contact Author)

Tohoku University ( email )

SKK Building, Katahira 2
Aoba-ku, Sendai, Miyagi 980-8577
Japan

Jun-ichi Itaya

Hokkaido University - Division of Modern Economics and Management ( email )

Sapporo 060-0809
Japan

Akitomo Yamanashi

Hokkaido University ( email )

5 Kita 8 Jonishi, Kita Ward
Hokkaido Prefecture
Sapporo, Hokkaido 060-0808
Japan

Tatsuyoshi Miyakoshi

Osaka University ( email )

1-1 Yamadaoka
Suita
Osaka, 565-0871
Japan

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