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Rock-Paper-Scissors, Differential Games and Biological Diversity [article]

Tung Mai and Ioannis Panageas and Will Ratcliff and Vijay V. Vazirani and Peter Yunker
2017 arXiv   pre-print
We model a situation in which a collection of species derive their fitnesses via a rock-paper-scissors-type game; however, the precise payoffs are a function of the environment.  ...  We cast our model in the setting of a differential game and we show that for a certain setting of parameters, this dynamics cycles.  ...  Acknowledgements Ioannis Panageas would like to acknowledge a MIT-SUTD postdoctoral fellowship and thank Georgios Piliouras for pointing out [18] and fruitful discussions.  ... 
arXiv:1710.11249v1 fatcat:caduc45y5bavrlqag5wukjrnhe

Taking the bad with the good

Carl T. Bergstrom, Benjamin Kerr
2015 Nature  
If Rock kills Scissors, Scissors kills Paper and Paper kills Rock, we have the standard situation (Fig. 1a) .  ...  They demonstrate mathematically how bystander protection can Figure 1 | Cyclical dynamics in a 'rock-paper-scissors' game with public goods. a, In a standard rock-paper-scissors game, rock beats scissors  ... 
doi:10.1038/nature14525 pmid:25992542 fatcat:bjpkzupbzfd25e4xdowrihxzyi

Nonlinear dynamics of the rock-paper-scissors game with mutations

Danielle F. P. Toupo, Steven H. Strogatz
2015 Physical Review E  
We analyze the replicator-mutator equations for the Rock-Paper-Scissors game.  ...  This attracting periodic solution exists for all the mutation patterns considered, and persists arbitrarily close to the limit of zero mutation rate and a zero-sum game.  ...  INTRODUCTION In the children's game of rock-paper-scissors, paper wraps rock, rock smashes scissors, and scissors cut paper.  ... 
doi:10.1103/physreve.91.052907 pmid:26066229 fatcat:5oxssl6ea5e7halidoqm6swuwu

Chaotic Dynamics in Asymmetric Rock-Paper-Scissors Games

Wenjun Hu, Gang Zhang, Haiyan Tian, Zhiwei Wang
2019 IEEE Access  
Using dynamical theory, we investigate chaotic behavior in asymmetric Rock-Paper-Scissors games under imitative dynamics with two different populations.  ...  INDEX TERMS Evolutionary game, imitative dynamics, chaos, rock-paper-scissors. 175614 This work is licensed under a Creative Commons Attribution 4.0 License.  ...  It is a famous three-strategy game, in which rock crushes scissors, scissors cut paper, and paper wraps rock.  ... 
doi:10.1109/access.2019.2956816 fatcat:pmaa6ojbnzfzvbyqoygnwvpwmu

Diverse Auto-Curriculum is Critical for Successful Real-World Multiagent Learning Systems [article]

Yaodong Yang, Jun Luo, Ying Wen, Oliver Slumbers, Daniel Graves, Haitham Bou Ammar, Jun Wang, Matthew E. Taylor
2021 arXiv   pre-print
In order to extend MARL methods to real-world domains outside of video games, we envision in this blue sky paper that maintaining a diversity-aware auto-curriculum is critical for successful MARL applications  ...  Specifically, we argue that behavioural diversity is a pivotal, yet under-explored, component for real-world multiagent learning systems, and that significant work remains in understanding how to design  ...  The central feature of such non-transitive relations can be thought of as analogous to a Rock-Paper-Scissors game, where rock beats scissors, scissors beats paper, and paper beats rock.  ... 
arXiv:2102.07659v2 fatcat:nlijvc7yizflvdz5iqxibw4tfa

Bacterial Games [chapter]

Erwin Frey, Tobias Reichenbach
2011 The Frontiers Collection  
Major research goals are to identify and understand mechanisms that ensures viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of "social" behavior.  ...  A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the mathematical tools and conceptual framework for a deeper understanding of these ecological  ...  We are indebted to Benjamin Andrae, Maximilian Berr, Jonas Cremer, Alexander Dobrinevsky, Anna Melbinger, Mauro Mobilia, Steffen Rulands, and Anton Winkler, with whom we had the pleasure to work on game  ... 
doi:10.1007/978-3-642-18137-5_13 fatcat:vnxjr5dpcngurimutxvlaavw7u

Rock-Paper-Scissors in the Chemostat

James P Braselton
2013 Journal of computer science and systems biology  
Rock-Paper-Scissors is a game played by two players to deter-mine a single winner. Biological relationships of Rock-Paper-Scissors are documented.  ...  Citation: Braselton JP, Abell ML, Braselton LM (2013) Rock-Paper-Scissors in the Chemostat.  ...  Therefore, the first author dedicates this paper to him.  ... 
doi:10.4172/jcsb.1000109 fatcat:yiaqdvifszfcjh4x2pblfdedui

A Five-Species Jungle Game

Yibin Kang, Qiuhui Pan, Xueting Wang, Mingfeng He, Gui-Quan Sun
2016 PLoS ONE  
In this paper, we investigate the five-species Jungle game in the framework of evolutionary game theory.  ...  We address the coexistence and biodiversity of the system using mean-field theory and Monte Carlo simulations.  ...  Wrote the paper: YK XW.  ... 
doi:10.1371/journal.pone.0157938 pmid:27332995 pmcid:PMC4917250 fatcat:b6dgilr7kvafxpd2lmda36wv6y

Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games

Tobias Reichenbach, Mauro Mobilia, Erwin Frey
2007 Nature  
Such non-transitive relations lead to an evolution with central features represented by the 'rock-paper-scissors' game, where rock crushes scissors, scissors cut paper, and paper wraps rock.  ...  However, population mobility is a central feature of real ecosystems: animals migrate, bacteria run and tumble. Here, we observe a critical influence of mobility on species diversity.  ...  Bathe and M. Leisner for inspiring discussions and helpful comments on the manuscript. Financial support of the German Excellence Initiative via the program  ... 
doi:10.1038/nature06095 pmid:17728757 fatcat:3dbriawvbbhbhbqoh7bltkmxo4

Competitive intransitivity, population interaction structure, and strategy coexistence

Robert A. Laird, Brandon S. Schamp
2015 Journal of Theoretical Biology  
rock-paper-scissors.  ...  Intransitive competition (as in the game rock-paper-scissors) promotes coexistence. Spatial structure can enhance intransitivity-mediated coexistence.  ...  Leventis, and S. Yazdani for technical assistance. We thank our editor and anonymous referees for their constructive comments.  ... 
doi:10.1016/j.jtbi.2014.10.010 pmid:25454011 fatcat:fnxzrnoykfeqzkvnwfkbespcs4

From pairwise to group interactions in games of cyclic dominance

Attila Szolnoki, Jeromos Vukov, Matjaž Perc
2014 Physical Review E  
We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change.  ...  going from single pair to group interactions in games of cyclic dominance.  ...  INTRODUCTION Rock is wrapped by paper, paper is cut by scissors, and scissors are broken by a rock.  ... 
doi:10.1103/physreve.89.062125 pmid:25019743 fatcat:yx3vpxfnirg37jb4io2dzboila

Spatial heterogeneity promotes coexistence of rock–paper–scissors metacommunities

Sebastian J. Schreiber, Timothy P. Killingback
2013 Theoretical Population Biology  
The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for  ...  For dispersal rates below d^*, the product of the invasion rates exceed the product of the exclusion rates and the rock-paper-scissor metacommunities persist regionally despite being extinction prone locally  ...  rock-paper-scissors game.  ... 
doi:10.1016/j.tpb.2013.02.004 pmid:23474219 fatcat:dtdzxaf2lzec5jdx7bxkzqb3g4

Many ways to stay in the game: individual variability maintains high biodiversity in planktonic microorganisms

S. Menden-Deuer, J. Rowlett
2014 Journal of the Royal Society Interface  
In nature, this variability can be observed as niche differentiation, variability in environmental and ecological factors, and variability of individual behaviors or physiology.  ...  We introduce a new game-theoretic model for competing micro-organisms in which one player consists of all organisms of one species.  ...  We thank Henry Segerman and Mick Follows for critical reading of this manuscript and the anonymous reviewers whose comments greatly improved this paper. Funding statement.  ... 
doi:10.1098/rsif.2014.0031 pmid:24647904 pmcid:PMC4006243 fatcat:evfoo3rbzjggxk3usjw4zcmgd4

Evolutionary game theory: cells as players

Sabine Hummert, Katrin Bohl, David Basanta, Andreas Deutsch, Sarah Werner, Günter Theißen, Anja Schroeter, Stefan Schuster
2014 Molecular Biosystems  
In this review we discuss numerous examples of applying game theory to cellular processes.  ...  The interaction of living cells can often be described by game theory, for example, in the case of secretion of extracellular enzymes.  ...  We thank Ina Weiß for helpful literature search and Sebastian Germerodt for stimulating discussions.  ... 
doi:10.1039/c3mb70602h pmid:25270362 fatcat:7up3voypqbe7logsgkzftw5biq

A Five Species Cyclically Dominant Evolutionary Game with Fixed Direction: A New Way to Produce Self-Organized Spatial Patterns

Yibin Kang, Qiuhui Pan, Xueting Wang, Mingfeng He
2016 Entropy  
Consider, for example, the rock-paper-scissors game.  ...  Mobilia studies rock-paper-scissors games including studying mechanisms [36] .  ...  The rock-paper-scissors game is also reflected in the strategic choice in terms of biological methods, for example, the mating strategy of side-blotched lizards [18] and the regular oscillations of the  ... 
doi:10.3390/e18080284 fatcat:j477qkw2tvb6ndu4ewalyl72xe
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