Efficiency May Improve When Defectors Exist

43 Pages Posted: 17 Oct 2013 Last revised: 2 Apr 2015

See all articles by Takako Fujiwara-Greve

Takako Fujiwara-Greve

Keio University - Faculty of Economics

Masahiro Okuno-Fujiwara

University of Tokyo - Faculty of Economics

Nobue Suzuki

Komazawa University

Multiple version iconThere are 2 versions of this paper

Date Written: April 1, 2015

Abstract

In repeated Prisoner's Dilemma, the C-trigger strategy played by all players is well-known to achieve symmetric efficiency when players are sufficiently patient. By contrast, if players are free to quit from a repeated Prisoner's Dilemma without information flow to new partners, cooperation from the outset of new partnerships cannot be a part of any symmetric equilibrium.

Fujiwara-Greve and Okuno-Fujiwara (2009) showed that symmetric trust-building strategies can constitute an equilibrium for sufficiently long initial (D,D) (trust-building) periods. However, trust-building periods create social loss of payoffs, and there is a possibility that an asymmetric equilibrium with some players cooperating immediately, while others defect, may be more efficient. We show that there is a "fundamentally asymmetric" locally stable Nash equilibrium consisting of the most cooperative strategy (C-trigger with ending the partnership when betrayed) and the most non-cooperative strategy, which plays D and ends the partnership immediately. When the deviation gain is relatively small, the fundamentally asymmetric equilibrium is neutrally stable against equilibrium entrants within trust-building strategies and is more efficient than any Nash equilibrium consisting of trust-building strategies. For example, in small scale transactions in virtual malls, starting honest transactions immediately with some risk of being betrayed is socially better than asking everyone to delay transactions and build up some trust. Our result indicates that behavioral diversity can be stable and beneficial for the society, even if players are free to escape from personalized punishments.

Keywords: efficiency, diversity, voluntary separation, Prisoner's Dilemma, endogenous partnerships

JEL Classification: C73

Suggested Citation

Fujiwara-Greve, Takako and Okuno-Fujiwara, Masahiro and Suzuki, Nobue, Efficiency May Improve When Defectors Exist (April 1, 2015). Available at SSRN: https://ssrn.com/abstract=2341019 or http://dx.doi.org/10.2139/ssrn.2341019

Takako Fujiwara-Greve (Contact Author)

Keio University - Faculty of Economics ( email )

2-15-45 Mita, Ninato-ku
Tokyo 1088345
Japan

Masahiro Okuno-Fujiwara

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Nobue Suzuki

Komazawa University ( email )

1-23-1 Komazawa
Setagaya-ku
Tokyo, 1548525
Japan

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