Repeated triangular trade: Sustaining circular cooperation with observation errors

Kota Shigedomi, Tadashi Sekiguchi, Atsushi Iwasaki, Makoto Yokoo

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We introduce a new fundamental problem called triangular trade, which is a natural extension of the well-studied prisoner’s dilemma for three (or more) players where a player cannot directly punish a seemingly defecting player. More specifically, this problem deals with a situation where the power/influence of players is one-way, players would be better off if they maintain circular cooperation, but each player has an incentive to defect. We analyze whether players can sustain such circular cooperation when they repeatedly play this game and each player observes the actions of another player with some observation errors (imperfect private monitoring). We confirm that no simple strategy can constitute an equilibrium within any reasonable parameter settings when there are only two actions: “Cooperate” and “Defect.” Thus, we introduce two additional actions: “Whistle” and “Punish,” which can be considered as a slight modification of “Cooperate.” Then, players can achieve sustainable cooperation using a simple strategy called Remote Punishment strategy (RP), which constitutes an equilibrium for a wide range of parameters. Furthermore, we show the payoff obtained by a variant of RP is optimal within a very general class of strategies that covers virtually all meaningful strategies.

Original languageEnglish
Title of host publicationPRIMA 2018
Subtitle of host publicationPrinciples and Practice of Multi-Agent Systems - 21st International Conference, 2018, Proceedings
EditorsNir Oren, Yuko Sakurai, Itsuki Noda, Tran Cao Son, Tim Miller, Bastin Tony Savarimuthu
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783030030971
Publication statusPublished - 2018
Event21st International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2018 - Tokyo, Japan
Duration: Oct 29 2018Nov 2 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11224 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other21st International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2018

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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