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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
<span title="2017-10-30">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We cast our model in the setting of a differential game and we show that for a certain setting of parameters, this dynamics cycles.  ...  Since the dynamics cycles, no species goes extinct and diversity is maintained.  ...  Acknowledgements Ioannis Panageas would like to acknowledge a MIT-SUTD postdoctoral fellowship and thank Georgios Piliouras for pointing out [18] and fruitful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.11249v1">arXiv:1710.11249v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/caduc45y5bavrlqag5wukjrnhe">fatcat:caduc45y5bavrlqag5wukjrnhe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200828063303/https://arxiv.org/pdf/1710.11249v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/47/f3/47f33d43376ef4f2e14a63d99ac455ca623509dc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.11249v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

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
<span title="2021-02-16">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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  ...  Therefore, creating an auto-curriculum in non-zero sum games is an open problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.07659v2">arXiv:2102.07659v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nlijvc7yizflvdz5iqxibw4tfa">fatcat:nlijvc7yizflvdz5iqxibw4tfa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210218014753/https://arxiv.org/pdf/2102.07659v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/38/fa/38fa4bd7e944b73d128b93f2d279416f93074222.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.07659v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Chaotic Dynamics in Asymmetric Rock-Paper-Scissors Games

Wenjun Hu, Gang Zhang, Haiyan Tian, Zhiwei Wang
<span title="">2019</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q7qi7j4ckfac7ehf3mjbso4hne" style="color: black;">IEEE Access</a> </i> &nbsp;
Our theoretical analysis and numerical simulations demonstrate that the dynamical system can give rise to chaotic behavior in zero-sum and positive-sum asymmetric games.  ...  However, chaos cannot occur in a negative-sum asymmetric game. In particular, the numerical simulations show that there is a limit cycle in a negative-sum asymmetric game.  ...  NUMERICAL SIMULATIONS In this section, we give two simulations for imitative dynamics with zero-sum and nonzero-sum games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/access.2019.2956816">doi:10.1109/access.2019.2956816</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pmaa6ojbnzfzvbyqoygnwvpwmu">fatcat:pmaa6ojbnzfzvbyqoygnwvpwmu</a> </span>
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Page 1900 of Mathematical Reviews Vol. 49, Issue 5 [page]

<span title="">1975</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Author’s summary: “Mixed strategy solutions are given for two-person, zero-sum games with payoff functions consisting of quadratic, bilinear, and linear terms, and strategy spaces consisting of closed  ...  The participants and invited speakers were | mathematicians interested in problems of a biological | nature, and scientists actively engaged in developing mathematical models in biological fields.  ... 
<span class="external-identifiers"> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_mathematical-reviews_1975-05_49_5/page/1900" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_mathematical-reviews_1975-05_49_5/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

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

Danielle F. P. Toupo, Steven H. Strogatz
<span title="2015-05-11">2015</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
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.  ...  After it loses stability, the coexistence state gives birth to a stable limit cycle solution created in a supercritical Hopf bifurcation.  ...  ROCK-PAPER-SCISSORS GAME The standard rock-paper-scissors game is a zero-sum game with payoff matrix given in Table I .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.91.052907">doi:10.1103/physreve.91.052907</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26066229">pmid:26066229</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5oxssl6ea5e7halidoqm6swuwu">fatcat:5oxssl6ea5e7halidoqm6swuwu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180118162109/https://static1.squarespace.com/static/5436e695e4b07f1e91b30155/t/5551e3d3e4b0f3050ceae36e/1431430099031/rock-paper-scissors-with-mutations.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ed/ff/edffbf73a581ebbe1fefad26f4bfa97aac982891.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.91.052907"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Modelling Behavioural Diversity for Learning in Open-Ended Games [article]

Nicolas Perez Nieves, Yaodong Yang, Oliver Slumbers, David Henry Mguni, Ying Wen, Jun Wang
<span title="2021-06-10">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on determinantal point processes (DPP).  ...  Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors).  ...  strategies, and the resulting strategies guarantee to converge to the NE in two-player zero-sum, or potential games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.07927v2">arXiv:2103.07927v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cpo6geyqorb3td57mqi2xu2skm">fatcat:cpo6geyqorb3td57mqi2xu2skm</a> </span>
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Many ways to stay in the game: individual variability maintains high biodiversity in planktonic microorganisms

S. Menden-Deuer, J. Rowlett
<span title="2014-03-19">2014</span> <i title="The Royal Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kdv34qlmv5gsfphm6vnme655ia" style="color: black;">Journal of the Royal Society Interface</a> </i> &nbsp;
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.  ...  Universität Hannover and the Australian National University.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1098/rsif.2014.0031">doi:10.1098/rsif.2014.0031</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24647904">pmid:24647904</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4006243/">pmcid:PMC4006243</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/evfoo3rbzjggxk3usjw4zcmgd4">fatcat:evfoo3rbzjggxk3usjw4zcmgd4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228084313/http://pdfs.semanticscholar.org/9f95/dd4376354ada5613603480acc333797d4085.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9f/95/9f95dd4376354ada5613603480acc333797d4085.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1098/rsif.2014.0031"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4006243" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

From Darwin to Poincaré and von Neumann: Recurrence and Cycles in Evolutionary and Algorithmic Game Theory [article]

Victor Boone, Georgios Piliouras
<span title="2019-10-03">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We provide a complete characterization of its behavior in zero-sum evolutionary games.  ...  In simple evolutionary zero-sum games, such as Rock-Paper-Scissors, replicator dynamic is periodic , however, its behavior in higher dimensions is not well understood.  ...  Limit behavior: Poincaré recurrence, cycles and convergence to boundary Zero-sum games with interior Nash are Poincaré recurrent We generalize previous result from [37] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.01334v1">arXiv:1910.01334v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qy2cwkxxbzhkra7wmfxzggwj54">fatcat:qy2cwkxxbzhkra7wmfxzggwj54</a> </span>
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Learning Dynamics and the Co-Evolution of Competing Sexual Species [article]

Georgios Piliouras, Leonard J. Schulman
<span title="2017-11-18">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These cycles stay bounded away from the boundary and thus, learning-dynamics competition between sexual species can provide an explanation for genetic diversity.  ...  Namely, the play of the many "selfish genes" implements a time-averaged correlated equilibrium where the average fitness of each species is exactly equal to its value in the two species zero-sum competition  ...  the zero-sum game.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1711.06879v1">arXiv:1711.06879v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nen5sun6ozhgfhfpknk2m7abf4">fatcat:nen5sun6ozhgfhfpknk2m7abf4</a> </span>
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Chaos as a Source of Complexity and Diversity in Evolution [article]

Kunihiko Kaneko
<span title="1993-11-25">1993</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game.  ...  A mechanism of maintenance of diversity, "homeochaos", is given in an ecological system with interaction among many species.  ...  The work is partially supported by Grant-in-Aids for Scientific Research from the Ministry of Education, Science, and Culture of Japan.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/adap-org/9311003v1">arXiv:adap-org/9311003v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bathfrt2abde7d5pyagq6qmmwy">fatcat:bathfrt2abde7d5pyagq6qmmwy</a> </span>
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Chaos as a Source of Complexity and Diversity in Evolution

Kunihiko Kaneko
<span title="">1993</span> <i title="MIT Press - Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/trtzv54dg5e5lpy55iml6bgv6u" style="color: black;">Artificial Life</a> </i> &nbsp;
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game.  ...  the emergence and maintenance of complexity and diversity, in order to understand the evolution of the complex "society" of life.  ...  The work is partially supported by Grant-in-Aids for Scientific Research from the Ministry of Education, Science, and Culture of Japan.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/artl.1993.1.163">doi:10.1162/artl.1993.1.163</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ubhqaa4egnha7n6uq6lcbvamoi">fatcat:ubhqaa4egnha7n6uq6lcbvamoi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211012100340/https://watermark.silverchair.com/artl.1993.1.1_2.163.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAtgwggLUBgkqhkiG9w0BBwagggLFMIICwQIBADCCAroGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQM9bjjByDv0HeTGjt3AgEQgIICi4reej63ZbRWZVh8pk8-9zb2JzoiqzByOBv7dYLYAfjaGk9SKsxIrCZRenl6JwznYeX2SFAvAurJdV0Ew6DPrsunb3iO9L_83ZV4tFP6ReMBh4J6Y_71ZI3bqrVkuTPoaa3zqqflhnwR2uRGiYjuI-GbPwfs9TZI2PX-D44SALLuVppoafKwhcXbU3KyKHaOxUlka_lXIMOAI0bYPFGusxclpkjmPFTo6KYBGuJ6PLhraUgQVa4ctSSTPKGNH3CvFaR8em_tXqLGqkNCwOHQg_VADvO5Ses86kcelgnSfaaehfkeBpad0SDDe_BEZBBcrgMhPU9Tl52c3qQoGdZx3MVbrcEauhBy7D3AH_1drkDtko2mou-syjHNpXmmTQC049vvqH2MCUdM0Pz33SsMInuCclFy2E23d8fNfundR1VcX27UVH8vNLTJzfF-dMUkfhkuKf76Py3dp4vX6hfcGjwLeBBU_VKnLaAGeQ4SOPE7AXZriVe2RTm03EtljgBPZu4YKmFlsHuBjc8aH6Hp6GF4ndH8qr39TkG9qh-0aUq8OhvmZyvEvQjfURega1pOgIIriC5PWzeyz69mdtG--ecuf6bJ5M0ZgFunnQbd_L5s7SOOhnjjpJiZEH3CPNEM9JXo6CzZqz41vR4iTgQl1DQP3QMx8bxHTWlR65xZiV_-6J_CY_38zdHSEXeGqHGDJ26ll1kppyrDKBMx6yxae9WeuFUBiA-xWbK6Oc2VUz46R7MuN23aZaabs5jKINC_a8YC5FQNRVIfUgjXcyuK58FXukrQt3cS3cHwf8QZlnk22Cul7iO_Wx_zeHz3UiOYOvq4Ohf3VGPxGPjoGlOHaU9cCqvfNyezGi27lg" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bc/e1/bce19f1af5b546ffe2e20346d7ed2035c85fcaeb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/artl.1993.1.163"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> mitpressjournals.org </button> </a>

The strength of diversity: mathematical proof that collections of variable individuals are robust in the face of challenges [article]

Julie Rowlett, Carl-Joar Karlsson, Medet Nursultanov
<span title="2021-12-06">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These equilibria suggest a mechanistic underpinning for biological and physical systems to tend towards increasing complexity and entropy, because diversity imparts strength to a system in competition  ...  Our first main contribution is a game theoretic framework for further analysis of the internal composition of an ensemble of individuals and the repercussions for the ensemble as a whole in competition  ...  In this work, diversity is a flexible concept that broadly means anything that differentiates.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.04054v3">arXiv:2108.04054v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pdfsjtcnljdodelbisdu6sqg4u">fatcat:pdfsjtcnljdodelbisdu6sqg4u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211208094834/https://arxiv.org/pdf/2108.04054v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/48/a2/48a2b99f04cf97009483e9cd2c29f50b12cd1af5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.04054v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The Signal Importance of Noise

Michael Macy, Milena Tsvetkova
<span title="2013-10-31">2013</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fue33oux2nfoldy2hc2w6ke6hy" style="color: black;">Sociological Methods &amp; Research</a> </i> &nbsp;
Contrary to widely held assumptions, these studies identify conditions in which noise can increase efficiency and predictability and reduce diversity.  ...  Noise is widely regarded as a residual category-the unexplained variance in a linear model or the random disturbance of a predictable pattern.  ...  Acknowledgment The authors wish to acknowledge the contributions of Michael Mäs, Andreas Flache, Dirk Helbing, and members of the Social Dynamics Laboratory at Cornell.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0049124113508093">doi:10.1177/0049124113508093</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fpi3xws4jzdyvb4hjmc4inop3q">fatcat:fpi3xws4jzdyvb4hjmc4inop3q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706060534/http://tsvetkova.me/wp-content/uploads/Macy-Tsvetkova_2013_Signal-Importance-of-Noise.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4b/24/4b24c841d5c77c4185989994c40f609017920446.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0049124113508093"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> sagepub.com </button> </a>

Global Change and Human Change: A Prescription for Adaptive Evolution from Ecological Network Theory [chapter]

B. C. Patten
<span title="2011-10-14">2011</span> <i title="WIT Press"> Ecodynamics: The Prigogine Legacy </i> &nbsp;
Indirect relations (epistemic, nonconservative and informational) develop automatically in transactional networks and introduce nonzero-sumness into the causal stream.  ...  Developing a network perspective on global change, ecology's 'AWFUL theorem', resulting from zero-sum transactions (ontic, conservative, energy-matter exchanges), is reviewed and illustrated by two examples  ...  Agents of cycling in ecosystems, such as saprovores and microbes, are important contributors to nonzero-sumness. 5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2495/978-1-84564-654-7/04">doi:10.2495/978-1-84564-654-7/04</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vgl7fziaozev3njc7ldq7rrogq">fatcat:vgl7fziaozev3njc7ldq7rrogq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200320143151/https://www.witpress.com/Secure/elibrary/papers/9781845646547/9781845646547004FU1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4d/49/4d493415929071b544ad5936db5c67decbae43dc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2495/978-1-84564-654-7/04"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Stability and diversity in collective adaptation

Yuzuru Sato, Eizo Akiyama, James P. Crutchfield
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jsigantcpjamteymlcjp25zyvq" style="color: black;">Physica D : Non-linear phenomena</a> </i> &nbsp;
We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics.  ...  Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors.  ...  EA was supported by the Grant-in-Aid for Young Scientists (B) No.14780342, The Ministry of Education, Culture, Sports, Science and Technology, Japan.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.physd.2005.06.031">doi:10.1016/j.physd.2005.06.031</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/foaptapilzcwtmb6id5cd5oh4e">fatcat:foaptapilzcwtmb6id5cd5oh4e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809004457/http://samoa.santafe.edu/media/workingpapers/04-08-025.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d0/ad/d0adad24b538a26ef4f86d094d4bf76d8bb97f11.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.physd.2005.06.031"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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