Cooperation and Control in Multiplayer Social Dilemmas. Hilbe, C., Wu, B., Traulsen, A., & Nowak, M. A. 111(46):16425–16430.
Cooperation and Control in Multiplayer Social Dilemmas [link]Paper  doi  abstract   bibtex   
[Significance] Many of the world's most pressing problems, like the prevention of climate change, have the form of a large-scale social dilemma with numerous involved players. Previous results in evolutionary game theory suggest that multiplayer dilemmas make it particularly difficult to achieve mutual cooperation because of the lack of individual control in large groups. Herein, we extend the theory of zero-determinant strategies to multiplayer games to describe which strategies maintain cooperation. Moreover, we propose two simple models of alliances in multiplayer dilemmas. The effect of these alliances is determined by their size, the strategy of the allies, and the properties of the social dilemma. When a single individual's strategic options are limited, forming an alliance can result in a drastic leverage. [Abstract] Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner's dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups.
@article{hilbeCooperationControlMultiplayer2014,
  title = {Cooperation and Control in Multiplayer Social Dilemmas},
  author = {Hilbe, Christian and Wu, Bin and Traulsen, Arne and Nowak, Martin A.},
  date = {2014-11},
  journaltitle = {Proceedings of the National Academy of Sciences},
  volume = {111},
  pages = {16425--16430},
  issn = {1091-6490},
  doi = {10.1073/pnas.1407887111},
  url = {https://doi.org/10.1073/pnas.1407887111},
  abstract = {[Significance] 

Many of the world's most pressing problems, like the prevention of climate change, have the form of a large-scale social dilemma with numerous involved players. Previous results in evolutionary game theory suggest that multiplayer dilemmas make it particularly difficult to achieve mutual cooperation because of the lack of individual control in large groups. Herein, we extend the theory of zero-determinant strategies to multiplayer games to describe which strategies maintain cooperation. Moreover, we propose two simple models of alliances in multiplayer dilemmas. The effect of these alliances is determined by their size, the strategy of the allies, and the properties of the social dilemma. When a single individual's strategic options are limited, forming an alliance can result in a drastic leverage. [Abstract] 

Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner's dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups.},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-13433379,~to-add-doi-URL,adaptive-control,cooperation,featured-publication,game-theory,multiplicity},
  number = {46}
}
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