@inproceedings{lanctot:nips:2017,
  booktitle = {NeurIPS},
author = {Marc Lanctot and Vinicius Zambaldi and Audrunas Gruslys and Angeliki Lazaridou and Karl
Tuyls and Julien Perolat and David Silver and Thore Graepel},
title = {A Unified Game Theoretic Approach to Multiagent Reinforcement Learning},
year = {2017},
OPTpublisher = {Curran Associates Inc.},
OPTaddress = {},
pages = {4190–4203},
numpages = {14},
OPTlocation = {},
OPTseries = {Neural Information Processing Systems}
}

@article{zagorsky:plosone:2013,
  author = 	 {Benjamin M. Zagorsky and Johannes G. Reiter and Krishnendu Chatterjee and Martin A. Nowak},
  title = 	 {Forgiver Triumphs in Alternating Prisoner's Dilemma},
  journal = 	 {PLOS ONE},
  year = 	 {2013},
  OPTkey = 	 {},
  volume = 	  {},
  number = 	  {},
  pages = 	 {1--8},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@article{hofbauer:mor:2009,
    author = {Hofbauer, Josef and Sorin, Sylvain and Viossat, Yannick},
    title = {Time Average Replicator and Best-Reply Dynamics},
    journal = {Mathematics of Operations Research},
    volume = {34},
    number = {2},
    pages = {263--269},
    year = {2009},
    OPTdoi = {10.1287/moor.1080.0359},
    OPTURL = {https://doi.org/10.1287/moor.1080.0359},
    OPTeprint = {https://doi.org/10.1287/moor.1080.0359},
    abstract = { Using an explicit representation in terms of the logit map, we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best-reply dynamics. }
}

@book{sutton1998rli,
  abstract = {This introductory textbook on reinforcement learning is targeted toward engineers and scientists in artificial intelligence, operations research, neural networks, and control systems, and we hope it will also be of interest to psychologists and neuroscientists. It also contains several new results. An html version is available.},
  added-at = {2008-09-26T11:05:09.000+0200},
  author = {Sutton, Richard S. and Barto, Andrew G.},
  biburl = {https://www.bibsonomy.org/bibtex/222063d43301bdff5387f812f3d59499b/yish},
  interhash = {9369ad4b6ab9e5aa15fb456143e9a09d},
  intrahash = {22063d43301bdff5387f812f3d59499b},
  keywords = {computational learning machine reinforcement supervised wleformativeeassessment},
  publisher = {MIT Press},
  timestamp = {2008-09-26T11:05:09.000+0200},
  title = {Reinforcement Learning: An Introduction},
  year = 1998
}

@article{nowak:science:2006,
author = {Nowak, Martin A.},
title= {Five rules for the evolution of cooperation},
journal = {Science},
year = {2006},
volume = {314},
number = {5805},
pages = {1560-1563}
}

@Article{fudenberg:ecma:1986,
  author = 	 {Drew Fudenberg and Eric Maskin},
  title = 	 {The Folk Theorem in Repeated Games with Discounting or with Incomplete Information},
  journal = 	 {Econometrica},
  year = 	 {1986},
  OPTkey = 	 {},
  volume = 	 {54},
  OPTnumber = 	 {},
  pages = 	 {533--554},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

 @InCollection{blum:agt:2007,
  author = 	 {Avrim Blum and Yishay Monsour},
  title = 	 {Learning, Regret minimization, and Equilibria},
  booktitle = 	 {Algorithmic game theory},
  OPTcrossref =  {},
  OPTkey = 	 {},
  pages = 	 {79--101},
  publisher = {Cambridge University Press},
  year = 	 {2007},
  OPTeditor = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTtype = 	 {},
  OPTchapter = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


@article{bowling:acm:2017,
author = {Bowling, Michael and Burch, Neil and Johanson, Michael and Tammelin, Oskari},
title = {Heads-up Limit Hold'em Poker is Solved},
year = {2017},
OPTissue_date = {November 2017},
OPTpublisher = {Association for Computing Machinery},
OPTaddress = {New York, NY, USA},
volume = {60},
number = {11},
OPTissn = {0001-0782},
OPTurl = {https://doi.org/10.1145/3131284},
OPTdoi = {10.1145/3131284},
OPTabstract = {Poker is a family of games that exhibit imperfect information, where players do not
have full knowledge of past events. While many perfect information games have been
solved (e.g., Connect-Four and checkers), no nontrivial imperfect information game
played competitively by humans has previously been solved. In this paper, we announce
that the smallest variant of poker in-play, heads-up limit Texas hold'em, is now essentially
weakly solved. Furthermore, this computation formally proves the common wisdom that
the dealer in the game holds a significant advantage. This result was enabled by a
new algorithm, CFR+, which is capable of solving extensive-form games three orders
of magnitude larger than previously possible. This paper is an extended version of
the original 2015 Science article, with additional results showing Cepheus' in-game
performance against computer and human opponents.},
journal = {Commun. ACM},
OPTmonth = oct,
pages = {81-–88},
OPTnumpages = {8}
}

@Article{brown:science:2019,
  title={Superhuman AI for multiplayer poker},
  author={Brown, Noam and Sandholm, Tuomas},
  journal={Science},
  volume={365},
  number={6456},
  pages={885--890},
  year={2019},
  publisher={American Association for the Advancement of Science}
}

@article{borgers:jet:1997,
title = {Learning Through Reinforcement and Replicator Dynamics},
journal = {Journal of Economic Theory},
volume = {77},
number = {1},
pages = {1-14},
year = {1997},
OPTissn = {0022-0531},
OPTdoi = {https://doi.org/10.1006/jeth.1997.2319},
OPTurl = {https://www.sciencedirect.com/science/article/pii/S002205319792319X},
author = {Tilman Börgers and Rajiv Sarin},
OPTabstract = {This paper considers a version of R. R. Bush and F. Mosteller's (1951,Psych. Rev.58, 313323; 1955, “Stochastic Models for Learning,” Wiley, New York) stochastic learning theory in the context of games. We show that in a continuous time limit the learning model converges to the replicator dynamics of evolutionary game theory. Thus we provide a non-biological interpretation of evolutionary game theory.Journal of Economic LiteratureClassification Numbers: C72, D83.}
}

@article{calvano:aer:2020,
Author = {Calvano, Emilio and Calzolari, Giacomo and Denicolò, Vincenzo and Pastorello, Sergio},
Title = {Artificial Intelligence, Algorithmic Pricing, and Collusion},
Journal = {American Economic Review},
Volume = {110},
Number = {10},
Year = {2020},
OPTMonth = {October},
Pages = {3267--3297},
OPTDOI = {10.1257/aer.20190623},
OPTURL = {https://www.aeaweb.org/articles?id=10.1257/aer.20190623}
}

@article{calvano:science:2020,
  title={Protecting consumers from collusive prices due to AI},
  author={Emilio Calvano and G. Calzolari and V. Denicol{\`o} and J. Harrington and S. Pastorello},
  journal={Science},
  year={2020},
  volume={370},
  pages={1040--1042}
}

 & Chaib-draa, 2009
@Article{burkov:ja:2009,
  author = 	 {Burkov, A. and Chaib-draa, B.},
  title = 	 {Effective learning in the presence of adaptive counterparts},
  journal = 	 {Journal of Algorithms},
  year = 	 {2009},
  OPTkey = 	 {},
  volume = 	 {64},
  number = 	 {4},
  pages = 	 {127--138},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

% Littman & Stone (2005)
@Article{littman:dss:2005,
  author = 	 {Michael L. Littman and Peter Stone},
  title = 	 {{A polynomial-time Nash equilibrium algorithm for repeated games}},
  journal = 	 {Decision Support Systems},
  year = 	 {2005},
  OPTkey = 	 {},
  volume = 	 {39},
  number = 	 {1},
  pages = 	 {55--66},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@article{borgs:geb:2010,
title = "The myth of the Folk Theorem ",
journal = "Games and Economic Behavior ",
volume = "70",
number = "1",
pages = "34 - 43",
year = "2010",
OPTnote = "Special Issue In Honor of Ehud Kalai ",
OPTissn = "0899-8256",
OPTdoi = "http://dx.doi.org/10.1016/j.geb.2009.04.016",
OPTurl = "http://www.sciencedirect.com/science/article/pii/S0899825609000785",
author = "Christian Borgs and Jennifer Chayes and Nicole Immorlica and Adam Tauman Kalai and Vahab Mirrokni and Christos Papadimitriou",
OPTkeywords = "Repeated games",
OPTkeywords = "Computable general equilibrium models "
}

@InProceedings{borgs:stoc:2008, 
  author = 	 {Borgs, C. and Chayes, J. and Immorlica, N. and Kalai, A. and 
Mirrokni, V. and Papadimitriou, C.}, 
  title = 	 {The myth of the folk theorem},
  OPTcrossref =  {},
  OPTkey = 	 {},
  booktitle = {Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC)},
  pages = 	 {365--372},
  year = 	 {2008},
  OPTeditor = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTmonth = 	 {},
  OPTorganization = {},
  OPTpublisher = {ACM Press},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@InCollection{shoham::2008,
  author = 	 {Yoav Shoham and Kevin Leyton-Brown},
  title = 	 {Learning and teaching},
  booktitle = 	 {Multiagent systems: Algorithmic, Game-Theoretic, and Logical Foundations},
  OPTcrossref =  {},
  OPTkey = 	 {},
  pages = 	 {189--222},
  publisher = {Cambridge University Press},
  year = 	 {2008},
  OPTeditor = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTtype = 	 {},
  OPTchapter = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@InProceedings{mescheder:bcai:2011,
  author = 	 {Daniel Mescheder and Karl Tuyls and Michael Kaisers}, 
  title = 	 {{POMDP} Opponent Models for Best Response Behavior},
  OPTcrossref =  {},
  OPTkey = 	 {},
  booktitle = {Proceedings of the 23rd Benelux Conference on Artificial Intelligence},
  OPTpages = 	 {},
  year = 	 {2011},
  OPTeditor = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTmonth = 	 {},
  OPTorganization = {},
  OPTpublisher = {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@InProceedings{wu:ijcai:2011, 
  author = 	 {F. Wu and S. Zilberstein and X. Chen. },
  title = 	 {Online Planning for Ad Hoc Autonomous Agent Teams},
  OPTcrossref =  {},
  OPTkey = 	 {},
  booktitle = {Proceedings of the 22th International Joint Conference on Artificial Intelligence (IJCAI)},
  pages = 	 {439--445},
  year = 	 {2011},
  OPTeditor = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTmonth = 	 {},
  OPTorganization = {},
  OPTpublisher = {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@inproceedings{andersen:aaai:2013,
	author = {Garrett Andersen and Vincent Conitzer},
	title = {Fast Equilibrium Computation for Infinitely Repeated Games},
	booktitle = {Proceedings of the 27th National Conference on Artificial Intelligence (AAAI)},
	year = {2013},
        pages = {53--59}, 
	OPTkeywords = {game theory; nash equilibrium; folk theorem; repeated games},
	OPTabstract = {It is known that an equilibrium of an infinitely repeated two-player game (with limit average payoffs) can be computed in polynomial time, as follows: according to the folk theorem, we compute minimax strategies for both players to calculate the punishment values, and subsequently find a mixture over outcomes that exceeds these punishment values. However, for very large games, even computing minimax strategies can be prohibitive. In this paper, we propose an algorithmic framework for computing equilibria of repeated games that does not require linear programming and that does not necessarily need to inspect all payoffs of the game. This algorithm necessarily sometimes fails to compute an equilibrium, but we mathematically demonstrate that most of the time it succeeds quickly on uniformly random games, and experimentally demonstrate this for other classes of games. This also holds for games with more than two players, for which no efficient general algorithms are known.},
	OPTurl = {https://www.aaai.org/ocs/index.php/AAAI/AAAI13/paper/view/6215/7062}
}

@INPROCEEDINGS{emery-montemerlo:aamas:2004,
    author = {Rosemary Emery-Montemerlo and Geoff Gordon and Jeff Schneider and Sebastian Thrun},
    title = {Approximate Solutions for Partially Observable Stochastic Games with Common Payoffs},
    booktitle = {Proceedings of the 3rd International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS)},
    year = {2004},
    pages = {136--143}
}

@Article{burkov:ker:2013,
  author = 	 {Andriy Burkov and Brahim Chaib-draa},
  title = 	 {Repeated Games for Multiagent Systems: A Survey},
  journal = 	 {The Knowledge Engineering Review},
  year = 	 {2013},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  pages = 	 {1--30},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

% Conitzer & Sandholm, 2007; 
@Article{conitzer:ml:2007,
  author = 	 {Conitzer, Vincent and Sandholm, Tuomas},
  title = 	 {{AWESOME: a general multiagent learning algorithm that converges in self-play and learns a best response against stationary opponents}},
  journal = 	 {Machine Learning},
  year = 	 {2007},
  OPTkey = 	 {},
  volume = 	 {67},
  number = 	 {1},
  pages = 	 {23--43},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@PHDTHESIS{Wiering1999ExplorationsIE,
  title={Explorations in efficient reinforcement learning},
  author={Wiering, Marco},
  year={1999},
  school={Universiteit van Amsterdam}
}

@book{Wiering2014Reinforcement,
author = {Wiering, Marco and van Otterlo, Martijn},
title = {Reinforcement Learning: State-of-the-Art},
year = {2014},
publisher = {Springer Publishing Company, Incorporated},
}


@InProceedings{mniha16asynchronous,
  title = 	 {Asynchronous Methods for Deep Reinforcement Learning},
  author = 	 {Mnih, Volodymyr and Badia, Adria Puigdomenech and Mirza, Mehdi and Graves, Alex and Lillicrap, Timothy and Harley, Tim and Silver, David and Kavukcuoglu, Koray},
  booktitle = 	 {Proceedings of the 33rd International Conference on Machine Learning (ICML)},
  pages = 	 {1928--1937},
  year = 	 {2016},
  month = 	 {20--22 Jun},
}

@article{wang2016acer,
  title={Sample efficient actor-critic with experience replay},
  author={Wang, Ziyu and Bapst, Victor and Heess, Nicolas and Mnih, Volodymyr and Munos, Remi and Kavukcuoglu, Koray and de Freitas, Nando},
  journal={arXiv preprint arXiv:1611.01224},
  year={2016}
}

@article{zhang2021multi,
  title={Multi-agent reinforcement learning: A selective overview of theories and algorithms},
  author={Zhang, Kaiqing and Yang, Zhuoran and Ba{\c{s}}ar, Tamer},
  journal={Handbook of Reinforcement Learning and Control},
  pages={321--384},
  year={2021},
  publisher={Springer}
}

@article{busoniu2008comprehensive,
  title={A comprehensive survey of multiagent reinforcement learning},
  author={Busoniu, Lucian and Babuska, Robert and De Schutter, Bart},
  journal={IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)},
  volume={38},
  number={2},
  pages={156--172},
  year={2008},
  publisher={IEEE}
}

@article{brown2018superhuman,
  title={Superhuman AI for heads-up no-limit poker: Libratus beats top professionals},
  author={Brown, Noam and Sandholm, Tuomas},
  journal={Science},
  volume={359},
  number={6374},
  pages={418--424},
  year={2018},
  publisher={American Association for the Advancement of Science}
}

@inproceedings{zinkevich2007regret,
  title={Regret minimization in games with incomplete information},
  author={Zinkevich, Martin and Johanson, Michael and Bowling, Michael and Piccione, Carmelo},
  booktitle = {NeurIPS},
  pages={1729--1736},
  year={2007}
}

@inproceedings{gordon2007no,
  title={No-regret algorithms for online convex programs},
  author={Gordon, Geoffrey J},
  booktitle = {Proceedings of the 19th Conference on Neural Information Processing Systems (NeurIPS)},
  pages={489--496},
  year={2006},
}

@Article{yong:2012,
  author = 	 {ヨンジュン ジョ and 岩崎 敦 and 神取 道宏 and 小原 一郎 and 横尾 真},
  title = {部分観測可能マルコフ決定過程を用いた私的観測付き繰り返しゲームにおける均衡分析プログラム},
  journal = {情報処理学会論文誌},
  year = 	 {2012},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  pages = 	 {1234--1246},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@InBook{axelrod:1987,
  author         = {Robert Axelrod},
  title          = {Genetic Algorithms and Simulated Annealing},
  year           = {1987},
  chapter        = {The Evolution of Strategies in the Iterated Prisoner's Dilemma},
  editor         = {Lawrence Davis},
  OPTpublisher      = {Morgan Kaufman, Los Altos, CA},
  pages          = {32--41},
  OPTannote         = {PDF copy I have is 2001 adaptation by Axelrod},
  OPTkey            = {axelrod-1987b}
}

@Article{hilbe:2013,
  author = 	 {Christian Hilbe and Martin A. Nowak and Karl Sigmund},
  title = 	 {Evolution of extortion in Iterated Prisoner's Dilemma games},
  OPTjournal = 	 {Proceedings of the National Academy of Sciences (PNAS)},
journal = 	 {Proceedings of the National Academy of Sciences},
year = 	 {2013},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  pages = 	 {6913--6918},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{kandori:2015,
  author = 	 {神取 道宏},
  ALTeditor = 	 {},
  title = 	 {人はなぜ協調するのか --くり返しゲーム理論入門--},
  OPTpublisher = 	 {公益財団法人 三菱経済研究所},
  publisher = 	 {三菱経済研究所},
  year = 	 {2015},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{kandori:2014,
  author = 	 {神取 道宏},
  ALTeditor = 	 {},
  title = 	 {ミクロ経済学の力},
  OPTpublisher = 	 {日本評論社},
  publisher = 	 {日本評論社},
  year = 	 {2014},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{okada:2011,
  author = 	 {岡田 章},
  ALTeditor = 	 {},
  title = 	 {ゲーム理論 新版},
  OPTpublisher = 	 {},
  publisher = 	 {有斐閣},
  year = 	 {2011},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{sekiguchi:2007,
  author = 	 {関口 格},
  ALTeditor = 	 {},
  title = 	 {経済セミナー増刊:ゲーム理論プラス, 「協調達成のための正しいお仕置きの仕方」},
  OPTpublisher = 	 {},
  publisher = 	 {日本評論社},
  year = 	 {2007},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{matsushima:2002,
  author = 	 {松島 斉},
  ALTeditor = 	 {},
  title = 	 {ゲーム理論の新展開},
  note = {第 4 章:「繰り返しゲームの新展開:私的モニタリングによる暗黙の協調」, pp.89-114},
  OPTpublisher = 	 {},
  publisher = 	 {勁草書房},
  year = 	 {2002},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{iba:2017,
  author = 	 {伊庭 斉志},
  ALTeditor = 	 {},
  title = 	 {人工知能の創発 知能の進化とシミュレーション},
  OPTpublisher = 	 {},
  publisher = 	 {株式会社 オーム社},
  year = 	 {2017},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}
@Book{sigmund:2010,
  author = 	 {Karl Sigmund},
  ALTeditor = 	 {},
  OPTtitle = 	 {The Calculus of Selfishness (Princeton Series in Theoretical and Computational Biology)},
  title = 	 {The Calculus of Selfishness},
  publisher = 	 {Princeton University Press},
  year = 	 {2010},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{abreu:econometrica:1990,
  author = 	 {Dilip Abreu and David Pearce and Ennio Stacchetti},
  title = 	 {Toward a Theory of Discounted Repeated Games with Imperfect Monitoring},
  journal = 	 {Econometrica},
  year = 	 {1990},
  OPTkey = 	 {},
  volume = 	 {58},
  OPTnumber = 	 {},
  pages = 	 {1041--1064},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

% Fudenberg and Levine (1994) "Efficiency and Observability with Long-Run and Short-run Players" JET, 62

@Article{fudenberg:econometrica:1994,
  author = 	 {D. Fudenberg and D. Levine and E. Maskin},
  title = 	 {The folk theorem with imperfect public information},
  journal = 	 {Econometrica},
  year = 	 {1994},
  OPTkey = 	 {},
  volume = 	 {62},
  OPTnumber = 	 {},
  pages = 	 {997--1040},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{sekiguchi:jet:1997,
  author = 	 {T. Sekiguchi},
  title = 	 {Efficiency in Repeated Prisoner's Dilemma with Private Monitoring},
  journal = 	 {Journal of Economic Theory},
  year = 	 {1997},
  OPTkey = 	 {},
  volume = 	 {76},
  OPTnumber = 	 {},
  pages = 	 {345--361},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


% Ely and Valimaki (2002) "A Robust Folk Theorem for the Prisoner's Dilemma" JET, 102

% Ely Horner and Olszeski (2005) "Belief-free equilibria" Econometrica, 73

@Article{ely:econo:2005,
  author = 	 {Jeffrey C. Ely and Johannes H\"{o}rner and Wojciech Olszewski},
  title = 	 {Belief-free equilibria in repeated games},
  journal = 	 {Econometrica},
  year = 	 {2005},
  OPTkey = 	 {},
  volume = 	 {73},
  number = 	 {2},
  pages = 	 {377--415},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

% Kandori and Obara (2004) "Efficiency in Repeated Games Revisited: The Role of Private Strategies" forthcoming in Econometrica

% Pearce (1992) "Repeated games: cooperation and rationality" in Advances in Economic Theory, sixth world congress

@InCollection{kandori:2010,
  author = 	 {Michihiro Kandori},
  editor = 	 {Steven N. Durlauf and Lawrence E. Blume},
  booktitle = 	 {Game theory},
  title = 	 {Repeated games},
  publisher = 	 {{Palgrave Macmillan}},
  year = 	 {2010},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTtype = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  pages = 	 {286--299},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


@inproceedings{tennenholtz:AAMAS:2009,
 author = {Tennenholtz, Moshe and Zohar, Aviv},
 title = {Learning equilibria in repeated congestion games},
 Optbooktitle = {AAMAS},
  booktitle = {Proceedings of the 8th International Joint Conference on Autonomous Agents and Multi-Agent System (AAMAS-09)},
 year = {2009},
 OPTisbn = {978-0-9817381-6-1},
 pages = {233--240},
 OPTlocation = {Budapest, Hungary},
 OPTpublisher = {International Foundation for Autonomous Agents and Multiagent Systems},
 OPTaddress = {Richland, SC},
 }

@inproceedings{doshi:aaai:2006,
  author    = {Prashant Doshi and Piotr J. Gmytrasiewicz},
  title     = {{On the Difficulty of Achieving Equilibrium in Interactive {POMDPs}}},
  OPTbooktitle = {AAAI},
  booktitle     = {Proceedings of the 21st National Conference on Artificial Intelligence (AAAI)},
  year      = {2006},
  pages     = {1131--1136}, 
  OPTcrossref  = {DBLP:conf/aaai/2006},
  OPTbibsource = {DBLP, http://dblp.uni-trier.de}
}

@inproceedings{ng:infocom:2008,
  author    = {See-Kee Ng and Winston Khoon Guan Seah},
  title     = {{Game-Theoretic Model for Collaborative Protocols in Selfish, Tariff-Free, Multihop Wireless Networks}},
  OPTbooktitle = {INFOCOM},
  booktitle = {27th Conference on Computer Communications}, 
  year      = {2008},
  pages     = {216-220},
  OPTee        = {http://dx.doi.org/10.1109/INFOCOM.2008.52},
  OPTcrossref  = {DBLP:conf/infocom/2008},
  OPTbibsource = {DBLP, http://dblp.uni-trier.de}
}

@inproceedings{wan:secon:2009,
  author={Wenjing Wang and Chatterjee, M. and Kwiat, K.},
  title={{Cooperation in Ad Hoc Networks with Noisy Channels}},
  booktitle={6th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks}, 
  year={2009},
  OPTmonth={june},
  OPTvolume={},
  OPTnumber={},
  pages={1--9},
  OPTkeywords={Nash Equilibrium;ad hoc network;channel noise;game theoretic solution;multihop data communication;packet forwarding process;state machine based strategy;ad hoc networks;game theory;wireless channels;},
  OPTdoi={10.1109/SAHCN.2009.5168920},
  OPTISSN={}
}


@Unpublished{kandori::2010,
  author = 	 {Michihiro Kandori and Ichiro Obara},
  title = 	 {{Towards a Belief-Based Theory of Repeated Games with Private Monitoring: An Application of {POMDP}}},
  note = 	 {mimeo, {\small http://mkandori.web.fc2.com/papers/KObb10June4.pdf}},
  OPTkey = 	 {},
  OPTmonth = 	 {},
  year = 	 {2010},
  OPTannote = 	 {}
}

@Article{kaelbling:ai:1998,
  author = 	 {Leslie Pack Kaelbling and Michael L. Littman and Anthony R. Cassandra},
  title = 	 {Planning and acting in partially observable stochastic domains},
  journal = 	 {Artificial Intelligence},
  year = 	 {1998},
  OPTkey = 	 {},
  volume = 	 {101},
  OPTnumber = 	 {},
  pages = 	 {99--134},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@article{matsushima:el:1991,
title = "On the theory of repeated games with private information : Part I: anti-folk theorem without communication",
journal = "Economics Letters",
volume = "35",
number = "3",
pages = "253 - 256",
year = "1991",
OPTnote = "",
OPTissn = "0165-1765",
OPTdoi = "DOI: 10.1016/0165-1765(91)90139-C",
OPTurl = "http://www.sciencedirect.com/science/article/B6V84-4590VMG-J3/2/b86b1179f56f204c597faaa23e75bb9b",
author = "Hitoshi Matsushima"
}

@Article{nowak:nature:1993, 
  author = 	 {Martin A. Nowak and Karl Sigmund},
  title = 	 {A strategy of win-stay, lose-shift that outperforms tit for tat in prisoner's dilemma},
  journal = 	 {Nature},
  year = 	 {1993},
  OPTkey = 	 {},
  volume = 	 {364},
  OPTnumber = 	 {},
  pages = 	 {56--58},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{kraines:jcr:1995,
  author = 	 {David Kraines and Vivian Kraines},
  title = 	 {{Evolution of Learning among Pavlov Strategies in a Competitive Environment with Noise}},
  journal = 	 {Journal of Conflict Resolution},
  year = 	 {1995},
  OPTkey = 	 {},
  volume = 	 {39},
  number = 	 {3},
  pages = 	 {439--466},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{ellison:res:1994,
  author={Ellison, Glenn},
  title={{Cooperation in the Prisoner's Dilemma with Anonymous Random Matching}},
  journal={Review of Economic Studies},
  year=1994,
  volume={61},
  number={3},
  pages={567-88},
  OPTmonth={July},
  OPTkeywords={ Environmental standards Abatement International trade MFN clause},
  OPTabstract={In this paper, we consider a three-stage game in the context of a competing exporters model to compare and contrast the effects of discriminatory and uniform (Most Favored Nation, MFN) tariffs on countries' choice over environmental standards for varying degrees of pollution spillovers. Because of the presence of punishment effects and stronger own and cross-tariff effects, we find that discrimination yields higher standards than MFN (and free trade) independently of the extent of pollution spillovers. When pollution is local and incentives to free ride on other countries' abatement efforts are weak, we show, however, that welfare is larger under MFN than under discrimination. In a dynamic setting, we consider the impact of symmetric and asymmetric treatments on the sustainability of an international environmental agreement (IEA) and obtain that multilateral cooperation is easier to sustain under discrimination than under MFN (or free trade).},
  OPTurl={http://ideas.repec.org/a/bla/restud/v61y1994i3p567-88.html}
}

@Book{rapoport:1965,
  author = 	 {Anatol Rapoport and Albert Chammah},
  title = 	 {Prisoner's Dilemma},
  publisher = 	 {University of Michigan Press},
  year = 	 {1965},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Book{fudenberg:1991,
  author = 	 {Drew Fudenberg and Jean Tirole},
  ALTeditor = 	 {},
  title = 	 {Game theory},
  publisher = 	 {MIT Press},
  year = 	 {1991},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{mailath:jet:2002, 
  author={Mailath, George J. and Morris, Stephen},
  title={Repeated Games with Almost-Public Monitoring},
  journal={Journal of Economic Theory},
  year=2002,
  volume={102},
  number={1},
  pages={189-228},
  OPTmonth={January},
  OPTkeywords={},
  OPTabstract={},
  OPTurl={http://ideas.repec.org/a/eee/jetheo/v102y2002i1p189-228.html}
}

@article {kraines:td:1989, 
   author = {Kraines, David and Kraines, Vivian},
   title = {Pavlov and the prisoner's dilemma},
   journal = {Theory and Decision},
   OPTpublisher = {Springer Netherlands},
   OPTissn = {0040-5833},
   OPTkeyword = {Business and Economics},
   pages = {47-79},
   volume = {26},
   issue = {1},
   OPTurl = {http://dx.doi.org/10.1007/BF00134056},
   OPTnote = {10.1007/BF00134056},
   year = {1989}
}


@Unpublished{phelan::2009,
  author = 	 {Christopher Phelan and Andrzej Skrzypacz},
  title = 	 {{Beliefs and Private Monitoring}},
  note = 	 {mimeo},
  OPTkey = 	 {},
  OPTmonth = 	 {},
  year = 	 {2009},
  OPTannote = 	 {}
}

@Article{phelan:res:2012, 
  author = 	 {Christopher Phelan and Andrzej Skrzypacz},
  title = 	 {{Beliefs and Private Monitoring}},
  journal = 	 {{Review of Economic Studies}},
  year = 	 {2012},
  OPTkey = 	 {},
  volume = 	 {79},
  number = 	 {4},
  pages = 	 {1637-1660},
  OPTmonth = 	 {},
  OPtnote = 	 {forthcoming},
  OPTannote = 	 {}
}

@book{AIM-2nd,
   author = {Russell, Stuart and Norvig, Peter},
   publisher = {Prentice Hall},
   title = {{Artificial Intelligence: A Modern Approach (2nd Edition)}},
   year = {2002}
}

@book{AIM-3rd,
   author = {Russell, Stuart and Norvig, Peter},
   publisher = {Prentice Hall},
   title = {{Artificial Intelligence: A Modern Approach (3rd Edition)}},
   year = {2009}
}

@Book{nowak:2006,
  author = 	 {Martin Nowak}, 
  ALTeditor = 	 {},
  title = 	 {Evolutionary Dynamics: Exploring the Equations of Life},
  publisher = 	 {Harvard University Press},
  year = 	 {2006},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@inproceedings{hansen:aaai:2004,
  author	= {Eric A. Hansen and Daniel S. Bernstein and Shlomo Zilberstein},
  title		= {Dynamic Programming for Partially Observable Stochastic Games},
  booktitle     = {Proceedings of the 19th National Conference on Artificial Intelligence (AAAI)},
  year		= {2004},
  pages		= {709-715},
  OPTaddress       = {San Jose, California},
  OPTurl		= {http://rbr.cs.umass.edu/shlomo/papers/HBZaaai04.html}
}

@INPROCEEDINGS{Hansen98solvingpomdps,
    author = {Eric A. Hansen},
    title = {Solving {POMDPs} by Searching in Policy Space},
    booktitle = {Proceedings of the Fourteenth International Conference on Uncertainty In Artificial Intelligence (UAI-98)},
    year = {1998},
    pages = {211--219}
}
@Book{mailath:2006,
  author = 	 {G. Mailath and L. Samuelson},
  title = 	 {Repeated Games and Reputation},
  publisher = 	 {Oxford University Press},
  year = 	 {2006},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTtype = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTpages = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


@Article{papadimitriou:mor:1987,
  author = 	 {Christos H. Papadimitriou and John N. Tsitsiklis},
  title = 	 {The Complexity of Markov Decision Processes},
  journal = 	 {Mathematics of Operations Research},
  year = 	 {1987},
  OPTkey = 	 {},
  volume = 	 {12},
  OPTnumber = 	 {},
  pages = 	 {441--450},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@inproceedings{nair03:jesp,
    author = {Ranjit Nair and Milind Tambe and Makoto Yokoo and David Pynadath and Stacy Marsella},
    title = {{Taming decentralized {POMDPs}: Towards efficient policy computation for multiagent settings}},
    booktitle = {Prodeedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-03)},
Optbooktitle = {IJCAI},
    year = 2003,
    Pages = {705--711},
    OPTurl = {citeseer.ist.psu.edu/nair03taming.html} 
}

@inproceedings{bernstein00:nexp,
    author = {Daniel S. Bernstein and Shlomo Zilberstein and Neil Immerman},
    title = {{The Complexity of Decentralized Control of Markov Decision Processes}},
    OPTbooktitle = {Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence (UAI-00)},
    booktitle = {UAI},
    pages = {32--37},
    year = 2000,
    url = {citeseer.nj.nec.com/bernstein00complexity.html}
}

@Article{rogers:tcs:2007,
  author = 	 {A. Rogers and R. K. Dash and S. D. Ramchurn and P. Vytelingum and N. R. Jennings},
  title = 	 {{Coordinating team players within a noisy iterated Prisoner's Dilemma tournament}},
  journal = 	 {Theoretical Computer Science},
  year = 	 {2007},
  OPTkey = 	 {},
  volume = 	 {377},
  number = 	 {1--3},
  pages = 	 {243--259},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@InProceedings{marecki:aamas:2008,
  author = 	 {Janusz Marecki and Tapana Gupta and Pradeep Varakantham and Milind Tambe and Makoto Yokoo},
  title = 	 {{Not All Agents Are Equal: Scaling up Distributed {POMDPs} for Agent Networks}},
  OPTcrossref =  {},
  OPTkey = 	 {},
  booktitle = {Proceedings of the 7th International Joint Conference on Autonomous Agents and Multi-Agent System (AAMAS-08)},
  pages = 	 {485--492},
  year = 	 {2008},
  OPTeditor = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTmonth = 	 {},
  OPTorganization = {},
  OPTpublisher = {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}



@Article{kalai:1988,
  author = 	 {Ehud Kalai and William Stanford},
  title = 	 {Finite Rationality and Interpersonal Complexity in Repeated Games},
  journal = 	 {Econometrica},
  year = 	 {1988},
  OPTkey = 	 {},
  volume = 	 {56},
  number = 	 {2},
  pages = 	 {387-410},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{RePEc:ecm:emetrp:v:50:y:1982:i:4:p:863-94,
  author={Kreps, David M. and Wilson, Robert},
  title={Sequential Equilibria},
  journal={Econometrica},
  year={1982},
  volume={50},
  number={4},
  pages={863-94},
  OPTmonth={July},
  OPTkeywords={},
  OPTabstract={No abstract is available for this item.},
  OPTurl={http://ideas.repec.org/a/ecm/emetrp/v50y1982i4p863-94.html},
  OPTkey = 	 {},
  OPThowpublished = {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


@Misc{cdd,
  OPTkey = 	 {},
  author = 	 {K. Fukuda},
  title = 	 {cdd and cdd+ Home Page},
  OPThowpublished = {},
  OPTmonth = 	 {},
  year = 	 {2012},
  howpublished = {http://www.ifor.math.ethz.ch/~fukuda/cdd\_home/},
  OPTurl={http://www.ifor.math.ethz.ch/~fukuda/cdd_home/},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


@inproceedings{Joe:aamas2012,
  author    = {Yongjoon Joe and
               Atsushi Iwasaki and
               Michihiro Kandori and
               Ichiro Obara and
               Makoto Yokoo},
  title     = {Automated equilibrium analysis of repeated games with private
               monitoring: a POMDP approach},
  booktitle={Proceedings of the 11th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS)},
  year      = {2012},
  pages     = {1305-1306},
}

@article{bhaskar:jet:2002,
title = "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring ",
journal = "Journal of Economic Theory ",
volume = "102",
number = "1",
pages = "40 - 69",
year = "2002",
OPTnote = "",
OPTissn = "0022-0531",
OPTdoi = "http://dx.doi.org/10.1006/jeth.2001.2878",
OPTurl = "http://www.sciencedirect.com/science/article/pii/S0022053101928789",
author = "V. Bhaskar and Ichiro Obara"
}

@Article{ely:jet:2002,
  author = 	 {Jeffrey C. Ely and Juuso V\"{a}lim\"{a}ki},
  title = 	 {A robust folk theorem for the prisoner's dilemma},
  journal = 	 {Journal of Economic Theory},
  year = 	 {2002},
  OPTkey = 	 {},
  volume = 	 {102},
  number = 	 {1},
  pages = 	 {84--105},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{horner:ecma:2006,
  author = 	 {Johannes H\"{o}rner and Wojciech Olszewski},
  title = 	 {The Folk Theorem for Games with Private Almost-Perfect Monitoring},
  journal = 	 {Econometrica},
  year = 	 {2006},
  OPTkey = 	 {},
  volume = 	 {74},
  OPTnumber = 	 {},
  pages = 	 {1499--1544},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{kandori:jet:2002,
  author = 	 {Michihiro Kandori},
  title = 	 {Introduction to Repeated Games with Private Monitoring},
  journal = 	 {Journal of Economic Theory},
  year = 	 {2002},
  OPTkey = 	 {},
  OPTvolume = 	 {102},
  OPTnumber = 	 {},
  OPTpages = 	 {1--15},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{kandori:ecma:1998,
  author = 	 {Michihiro Kandori and Hitoshi Matsushima},
  title = 	 {Private Observation, Communication and Collusion},
  journal = 	 {Econometrica},
  year = 	 {1998},
  OPTkey = 	 {},
  volume = 	 {66},
  OPTnumber = 	 {},
  pages = 	 {627--652},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{matsushima:ecma:2004,
  author = 	 {Hitoshi Matsushima},
  title = 	 {Repeated Games with Private Monitoring: Two Players},
  journal = 	 {Econometrica},
  year = 	 {2004},
  OPTkey = 	 {},
  volume = 	 {72},
  OPTnumber = 	 {},
  pages = 	 {823--852},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@article {kandori:ecma:2006,
author = {Kandori, Michihiro and Obara, Ichiro},
title = {Efficiency in Repeated Games Revisited: The Role of Private Strategies},
journal = {Econometrica},
volume = {74},
number = {2},
OPTpublisher = {Blackwell Publishing Ltd},
OPTissn = {1468-0262},
OPTurl = {http://dx.doi.org/10.1111/j.1468-0262.2006.00669.x},
OPTdoi = {10.1111/j.1468-0262.2006.00669.x},
pages = {499--519},
OPTkeywords = {Efficiency, imperfect public monitoring, mixed strategy, partnership game, private equilibrium, private strategy, repeated game, two-state machine},
year = {2006},
}

@Article{piccione:jet:2002,
  author = 	 {Michele Piccione},
  title = 	 {The Repeated Prisoner's Dilemma with Imperfect Private Monitoring},
  journal = 	 {Journal of Economic Theory},
  year = 	 {2002},
  OPTkey = 	 {},
  volume = 	 {102},
  OPTnumber = 	 {},
  pages = 	 {70--83},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{kalai:ecma-subjective:1993,
  author = 	 {Ehud Kalai and Ehud Lehrer},
  title = 	 {Subjective Equilibrium in Repeated Games},
  journal = 	 {Econometrica},
  year = 	 {1993},
  OPTkey = 	 {},
  volume = 	 {61},
  number = 	 {5},
  pages = 	 {1231--1240},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{blackwell:ams:1962,
  author = 	 {David Blackwell and Lester Dubins},
  title = 	 {Merging of opinions with increasing information},
  journal = 	 {The Annals of Mathematical Statistics},
  year = 	 {1962},
  OPTkey = 	 {},
  volume = 	 {33},
  number = 	 {3},
  pages = 	 {882--886},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Article{kalai:ecma:1993,
  author = 	 {Ehud Kalai and Ehud Lehrer},
  title = 	 {Rational learning leads to Nash equilibrium},
  journal = 	 {Econometrica},
  year = 	 {1993},
  OPTkey = 	 {},
  volume = 	 {61},
  number = 	 {5},
  pages = 	 {1019--1045},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Book{hoel::1972,
  author = 	 {Paul G. Hoel and Sidney C. Port and Charles J. Stone},
  ALTeditor = 	 {},
  title = 	 {Introduction to Stochastic Processes},
  publisher = 	 {Houghton Mifflin Company},
  year = 	 {1972},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}


@Article{fudenberg:jet:1991,
  author = 	 {Drew Fudenberg and David Levine},
  title = 	 {An Approximate Folk Theorem with Imperfect Private Information},
  journal = 	 {Journal of Economic Theory},
  year = 	 {1991},
  OPTkey = 	 {},
  volume = 	 {54},
  OPTnumber = 	 {},
  pages = 	 {26--47},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@article{MaynardSmith:1973,
  abstract = {Conflicts between animals of the same species usually are of "limited war" type, not causing serious injury. This is often explained as due to group or species selection for behaviour benefiting the species rather than individuals. Game theory and computer simulation analyses show, however, that a "limited war" strategy benefits individual animals as well as the species.},
  added-at = {2011-01-13T13:26:10.000+0100},
  author = {{Maynard Smith}, J. and Price, G. R.},
  biburl = {https://www.bibsonomy.org/bibtex/2eb73f9da4a6c8e315ba19cca9aa6d3ea/rincedd},
  description = {The Logic of Animal Conflict},
  doi = {10.1038/246015a0},
  file = {MaynardSmith1973 - The Logic of Animal Conflict.pdf:Evolutionary Game Theory/MaynardSmith1973 - The Logic of Animal Conflict.pdf:PDF},
  interhash = {039293276bad10d16afaa0da2f94cc57},
  intrahash = {eb73f9da4a6c8e315ba19cca9aa6d3ea},
  journal = {Nature},
  keywords = {game-theory evolution},
  number = 5427,
  pages = {15--18},
  timestamp = {2011-01-13T13:26:10.000+0100},
  title = {The Logic of Animal Conflict},
  volume = 246,
  year = 1973
}
@article{epubwu5590,
          volume = {97},
          number = {3},
          author = {Ulrich Berger},
           title = {Simple scaling of cooperation in donor-recipient games},
       publisher = {Elsevier},
            year = {2009},
         journal = {BioSystems},
           pages = {165--167},
        keywords = {Prisoner's Dilemma, Evolutionary game, Cooperation, Donor-recipient game},
             url = {http://epub.wu.ac.at/5590/},
        abstract = {We present a simple argument which proves a general version of the scaling phenomenon recently observed in donor-recipient games by Tanimoto ?Tanimoto, J., 2009. A simple scaling of the effectiveness of supporting mutual cooperation in donor-recipient games by various reciprocity mechanisms. BioSystems 96, 29-34?.}
}

@article{Taylor78evolutionarilystable,
    author = {Peter D. Taylor and Leo B. Jonker},
    title = {Evolutionarily Stable Strategies and Game Dynamics},
    journal = {Mathematical Biosciences},
    year = {1978},
    pages = {145--156}
}
@incollection{ohtsuki:2012,
  author      = {大槻 久},
  title       = {有限集団における進化ゲーム理論の発展},
  editor      = {},
  booktitle   = {特集「多様性と進化の統計解析」},
  publisher   = {統計数理研究所},
  address     = {},
  year        = {2012},
  pages       = {251-262},
  chapter     = {60-2},
}
@MISC{Beaufils97ourmeeting,
    author = {Bruno Beaufils and Jean-paul Delahaye and Philippe Mathieu},
    title = {Our Meeting With Gradual: A Good Strategy For The Iterated Prisoner's Dilemma},
    year = {1997}
}

@book{Hofbauer1998,
  added-at = {2011-01-13T13:25:56.000+0100},
  address = {Cambridge},
  author = {Hofbauer, Josef and Sigmund, Karl},
  biburl = {https://www.bibsonomy.org/bibtex/2575d159a617bae522cfb5410bac09120/rincedd},
  interhash = {d6f4dbba75ea1ae6192bb777b34b677b},
  intrahash = {575d159a617bae522cfb5410bac09120},
  keywords = {game-theory evolution},
  publisher = {Cambridge University Press},
  timestamp = {2011-01-13T13:25:57.000+0100},
  title = {Evolutionary Games and Population Dynamics},
  year = 1998
}
@inproceedings{Mathieu:2015,
 author = {Mathieu, Philippe and Delahaye, Jean-Paul},
 title = {New Winning Strategies for the Iterated Prisoner's Dilemma},
 booktitle = {Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems},
 series = {AAMAS '15},
 year = {2015},
 isbn = {978-1-4503-3413-6},
 location = {Istanbul, Turkey},
 pages = {1665--1666},
 numpages = {2},
 url = {http://dl.acm.org/citation.cfm?id=2772879.2773375},
 acmid = {2773375},
 publisher = {International Foundation for Autonomous Agents and Multiagent Systems},
 address = {Richland, SC},
 keywords = {agent's behaviour, game theory, group strategy, ipd, iterated prisoner's dilemma, memory, opponent identification},
} 

@Book{KL,
  author = 	 {Thomas M. Cover, Joy A. Thomas},
  ALTeditor = 	 {},
  title = 	 {ELEMENTS OF INFORMATION THEORY second edition},
  OPTpublisher = 	 {},
  publisher = 	 {John Wiley \& Sons, Inc.},
  year = 	 {2006},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTseries = 	 {},
  OPTaddress = 	 {},
  OPTedition = 	 {},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@Misc{scipy,
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author = {Srinivasan, Sriram and Lanctot, Marc and Zambaldi, Vinicius and P\'{e}rolat, Julien and Tuyls, Karl and Munos, R\'{e}mi and Bowling, Michael},
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  title={Learning from delayed rewards},
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@article{Bauer:2019,
author = {Bauer, Johann  and Broom, Mark  and Alonso, Eduardo },
title = {The stabilization of equilibria in evolutionary game dynamics through mutation: mutation limits in evolutionary games},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
volume = {475},
number = {2231},
pages = {20190355},
year = {2019},
OPTdoi = {10.1098/rspa.2019.0355},

OPTURL = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2019.0355},
OPTeprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2019.0355}
,
    OPTabstract = { The multi-population replicator dynamics is a dynamic approach to coevolving populations and multi-player games and is related to Cross learning. In general, not every equilibrium is a Nash equilibrium of the underlying game, and the convergence is not guaranteed. In particular, no interior equilibrium can be asymptotically stable in the multi-population replicator dynamics, e.g. resulting in cyclic orbits around a single interior Nash equilibrium. We introduce a new notion of equilibria of replicator dynamics, called mutation limits, based on a naturally arising, simple form of mutation, which is invariant under the specific choice of mutation parameters. We prove the existence of mutation limits for a large class of games, and consider a particularly interesting subclass called attracting mutation limits. Attracting mutation limits are approximated in every (mutation-)perturbed replicator dynamics, hence they offer an approximate dynamic solution to the underlying game even if the original dynamic is not convergent. Thus, mutation stabilizes the system in certain cases and makes attracting mutation limits near attainable. Hence, attracting mutation limits are relevant as a dynamic solution concept of games. We observe that they have some similarity to Q-learning in multi-agent reinforcement learning. Attracting mutation limits do not exist in all games, however, raising the question of their characterization. }
}


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journal = {BULLETIN OF MATHEMATICAL BIOLOGY},
month = {11},
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	OPTcopyright = {Springer Science+Business Media, Inc.},
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	journal = {Autonomous Agents and Multi-Agent Systems},
	OPTkeywords = {multi-agent systems; iterated games; reinforcement learning; Evolutionary Game Theory; COllective INtelligence},
	OPTlanguage = {English},
	OPTnote = {Author funded by a doctoral grant of the institute for advancement of scientific technological research in Flanders (IWT).},
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