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• {"link"=>{"url"=>"http://www.citeulike.org/user/andreassorge/article/5984610"}, "post_time"=>"2009-10-22 12:56:04", "tag"=>["game_theory", "networks"], "linkout"=>{"type"=>"DOI", "url"=>"http://dx.doi.org/10.1371/journal.pone.0001917"}, "username"=>"andreassorge", "article_id"=>"5984610"}

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{"title"=>"Learning and innovative elements of strategy adoption rules expand cooperative network topologies", "type"=>"journal", "authors"=>[{"first_name"=>"Shijun", "last_name"=>"Wang", "scopus_author_id"=>"8585423900"}, {"first_name"=>"Máté S.", "last_name"=>"Szalay", "scopus_author_id"=>"16305506100"}, {"first_name"=>"Changshui", "last_name"=>"Zhang", "scopus_author_id"=>"7405490589"}, {"first_name"=>"Peter", "last_name"=>"Csermely", "scopus_author_id"=>"8916910300"}], "year"=>2008, "source"=>"PLoS ONE", "identifiers"=>{"sgr"=>"44849126465", "doi"=>"10.1371/journal.pone.0001917", "pui"=>"351984128", "pmid"=>"18398453", "scopus"=>"2-s2.0-44849126465", "issn"=>"19326203", "isbn"=>"1932-6203 (Electronic)"}, "id"=>"4cdc458f-f015-3e53-9a07-0a44d83f61e7", "abstract"=>"Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoner's Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules, when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the re-organization of real-world networks, and may play a prominent role in the evolution of self-organizing, complex systems.", "link"=>"http://www.mendeley.com/research/learning-innovative-elements-strategy-adoption-rules-expand-cooperative-network-topologies", "reader_count"=>63, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>7, "Librarian"=>1, "Researcher"=>10, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>21, "Student > Postgraduate"=>3, "Student > Master"=>4, "Other"=>1, "Student > Bachelor"=>3, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>2, "Professor"=>5}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>7, "Librarian"=>1, "Researcher"=>10, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>21, "Student > Postgraduate"=>3, "Student > Master"=>4, "Other"=>1, "Student > Bachelor"=>3, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>2, "Professor"=>5}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Agricultural and Biological Sciences"=>17, "Business, Management and Accounting"=>4, "Computer Science"=>14, "Decision Sciences"=>1, "Economics, Econometrics and Finance"=>1, "Engineering"=>1, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>3, "Medicine and Dentistry"=>4, "Physics and Astronomy"=>8, "Psychology"=>1, "Social Sciences"=>4}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Social Sciences"=>{"Social Sciences"=>4}, "Decision Sciences"=>{"Decision Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Psychology"=>{"Psychology"=>1}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>4}, "Engineering"=>{"Engineering"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>17}, "Computer Science"=>{"Computer Science"=>14}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>4}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}}, "reader_count_by_country"=>{"Romania"=>1, "Hungary"=>4, "United States"=>2, "Japan"=>1, "Brazil"=>1, "United Kingdom"=>2, "Switzerland"=>3, "Germany"=>1}, "group_count"=>4}

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• http://doi.org/10.1016/j.physa.2014.07.013
• http://doi.org/10.1016/j.plrev.2015.04.033
• http://doi.org/10.1103/PhysRevE.78.031919
• http://doi.org/10.1016/j.chaos.2012.01.004
• http://doi.org/10.1016/j.amc.2015.03.018
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• http://doi.org/10.1142/S0219525914500118
• http://doi.org/10.1088/1742-6596/1012/1/012009

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• {"type"=>"COMMENT", "annotationUri"=>"info:doi/10.1371/annotation/631225a4-dd4d-4908-a282-0c2d482692c5", "title"=>"Referee comments: Referee 1 (Bence Toth)", "body"=>"Referee 1's review (Bence Toth):\n\n**********\nN.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication the manuscript has been revised in light of these comments and to address other editorial requirements.\n**********\n\nThe paper is very interesting, studying the effect of different strategy adoption scenarios on the ratio of cooperating subjects in repeated Prisoner's Dilemma and Hawk-Dove games on several network topologies. The authors analysed both short-term and long-term strategy adoption rules as well as reinforcement learning (Q-learning) on small world and scale free networks.\n\nThe main points of the authors are the following:\nCooperation is very sensitive to the topology of the network in case of short-term learning rules, but can be stabilised by introducing reinforcement learning. Long term learning strategies enhance cooperation on different topologies, but a certain level of randomness (innovation) has to be added to the system for stabilising the cooperation level.\n\nThe authors present a large amount of new results, and, together with this, naturally leave some points unanswered:\n\n* It would be good to see some quantitative analysis on the optimal level of P_innovation apart from the statement that an intermediate probability yields the optimum. This study might need some analytical computation, out of the scope of this paper. \n\n* On Figure S1, in panel (A),(C) and (D), for some of the curves a kind of \"phase transition like behaviour\" can be seen. Still in Figure S1, in panel (E), for p=0 we see a certain non-monotonicity (a peak around G=0.8). Some comments or analysis on these properties could be interesting.\n\n* In the captions of many figures, instead of pointing the reader to the section describing the methods, it would be more useful to give a brief explanation of the results shown in the plots.\n\n* Please change Figure 3 and Figure S9. They are barely visible. (Possibly, simply rescaling them.)\n\nThe results presented give important contribution to the existing literature of evolutionary games on networks and are clearly written. The methods are discussed in details, giving the reader the possibility of continuing the research.\nI recommend its publication in PlosOne.", "isRemoved"=>false, "created"=>"2008-04-10T15:49:44Z", "lastModified"=>"2008-04-10T15:49:44Z", "creator"=>{"userId"=>"80539"}, "highlightedText"=>"", "competingInterestStatement"=>{"creatorWasPrompted"=>false, "hasCompetingInterests"=>false}, "parentArticle"=>{"doi"=>"info:doi/10.1371/journal.pone.0001917", "state"=>"published", "journals"=>{"PLoSONE"=>{"journalKey"=>"PLoSONE", "eIssn"=>"1932-6203", "title"=>"PLOS ONE"}}}, "replyTreeSize"=>0, "mostRecentActivity"=>"2008-04-10T15:49:44Z", "replies"=>[]}
• {"type"=>"COMMENT", "annotationUri"=>"info:doi/10.1371/annotation/b2849314-2ee1-427c-a197-d276ddb1cb69", "title"=>"Acknowledgment of additional support", "body"=>"Part of the work of this paper has also been supported by the National Science Foundation of China (NSFC-60721003). The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript .", "highlightedText"=>"''.''\nhttp://plosone.org/article/info:doi/10.1371/journal.pone.0001917#article1.front1.article-meta1.abstract1.p1", "isRemoved"=>false, "created"=>"2008-04-12T12:13:09Z", "lastModified"=>"2008-04-12T12:13:09Z", "creator"=>{"userId"=>"117255"}, "competingInterestStatement"=>{"creatorWasPrompted"=>false, "hasCompetingInterests"=>false}, "parentArticle"=>{"doi"=>"info:doi/10.1371/journal.pone.0001917", "state"=>"published", "journals"=>{"PLoSONE"=>{"journalKey"=>"PLoSONE", "eIssn"=>"1932-6203", "title"=>"PLOS ONE"}}}, "replyTreeSize"=>0, "mostRecentActivity"=>"2008-04-12T12:13:09Z", "replies"=>[]}

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Figshare

• {"files"=>["https://ndownloader.figshare.com/files/933500"], "description"=>"<p>(Top middle panel) The small-world (spheres) and scale-free (cones) model networks were built as described in the legends of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#pone-0001917-g001\" target=\"_blank\">Figures 1</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#pone-0001917-g002\" target=\"_blank\">2</a>. The rewiring probability, <i>p</i> of the links of the original regular lattices giving small-world networks was increased from 0 to 1 with 0.05 increments, the number of edges linking each new node to former nodes in scale-free networks was varied from 1 to 7, and the means of shortest path-lengths and clustering coefficients were calculated for each network. Cubes and cylinders denote regular (p = 0) and random (p = 1.0) extremes of the small-world networks, respectively. For the description of the canonical repeated Prisoner's Dilemma game, as well as the best-takes-over (green symbols); long-term learning best-takes-over (blue symbols); long-term learning innovative best-takes-over (magenta symbols) and Q-learning (red symbols) strategy adoption rules used, see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#s4\" target=\"_blank\">Methods</a> and the ESM1. For each network 100 random runs of 5,000 time steps were executed at a fixed <i>T</i> value of 3.5. (Left and right panels) 2D side views of the 3D top middle panel showing the proportion of cooperators as the function of the mean length of shortest paths or the mean clustering coefficient, respectively. (Bottom middle panel) Color-coded illustration of the various network topologies used on the top middle panel. Here the same simulations are shown as on the top middle panel with a different color-code emphasizing the different network topologies. The various networks are represented by the following colors: regular networks – blue; small-world networks – green; scale-free networks – yellow; random networks – red (from the angle of the figure the random networks are behind some of the small-world networks and, therefore are highlighted with a red arrow to make there identification easier). The top middle panel and its side views show that the best-takes-over strategy adoption rule (green symbols) at this high temptation level results in a zero (or close-to-zero) cooperation. As opposed to this, the long-term best-takes-over strategy adoption rule (blue symbols) raise the level of cooperation significantly above zero, but the individual values vary greatly at the different network topologies. When the long-term strategy adoption rule is combined with a low level of randomness (magenta symbols) the cooperation level stays in most cases uniformly and its variation becomes high greatly diminished. Q-learning stabilizes cooperation further even at regular networks, which otherwise give an extremely variable outcome.</p>", "links"=>[], "tags"=>["elements", "applied"], "article_id"=>603944, "categories"=>["Physics", "Biochemistry"], "users"=>["Shijun Wang", "Máté S. Szalay", "Changshui Zhang", "Peter Csermely"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0001917.g003", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Long_term_learning_and_innovative_elements_of_strategy_adoption_rules_when_applied_together_allow_cooperation_in_a_large_number_of_model_networks_/603944", "title"=>"Long-term learning and innovative elements of strategy adoption rules, when applied together allow cooperation in a large number of model networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-09 01:05:44"}
• {"files"=>["https://ndownloader.figshare.com/files/933311"], "description"=>"<p>The modified Watts-Strogatz small-world network was built on a 15×15 lattice, where each node was connected to its eight nearest neighbors. The rewiring probabilities of the links placed originally on a regular lattice were 0.01 (left panels) and 0.04 (right panels), respectively. For the description of the canonical repeated Prisoner's Dilemma game, as well as the best-takes-over (top panels) and Q-learning (bottom panels) strategy adoption rules see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#s4\" target=\"_blank\">Methods</a> and the ESM1. The temptation level, T was 3.6. Networks showing the last round of 5,000 plays were visualized using the Kamada-Kawai algorithm of the Pajek program <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#pone.0001917-Batagelj1\" target=\"_blank\">[46]</a>. Dark blue dots and diamonds correspond to cooperators and defectors, respectively. The Figure shows that both the extent and distribution of cooperators vary, when using the best-takes-over strategy adoption rule (see top panels), while they are rather stable with the Q-learning strategy update rule (see bottom panels).</p>", "links"=>[], "tags"=>["q-learning", "improves", "stabilizes", "agents", "small-world", "networks"], "article_id"=>603747, "categories"=>["Physics", "Biochemistry"], "users"=>["Shijun Wang", "Máté S. Szalay", "Changshui Zhang", "Peter Csermely"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0001917.g001", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_long_term_learning_adoption_rule_Q_learning_improves_and_stabilizes_cooperation_of_agents_forming_various_small_world_networks_in_Prisoner_8217_s_Dilemma_games_/603747", "title"=>"A long-term learning adoption rule, Q-learning improves and stabilizes cooperation of agents forming various small-world networks in Prisoner’s Dilemma games.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-09 01:02:27"}
• {"files"=>["https://ndownloader.figshare.com/files/933398"], "description"=>"<p>Small-world (SW, filled, red symbols) networks were built as described in the legend of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#pone-0001917-g001\" target=\"_blank\">Figure 1</a>. The Barabasi-Albert-type scale-free networks (SF, open, blue symbols) contained 2,500 nodes, where at each construction step a new node was added with 3 new links attached to the existing nodes. For the description of the canonical repeated Prisoner's Dilemma game, as well as that of the best-takes-over (triangles, all panels), the Q-learning (rectangles, top panel) the best-takes-over long (circles, middle panel), and the best-takes-over long innovative (crosses, P_innovation = 0.0002, bottom panel) strategy adoption rules, see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0001917#s4\" target=\"_blank\">Methods</a> and the ESM1. For each strategy adoption rules and <i>T</i> temptation values 100 random runs of 5,000 time steps were executed. The figure shows that long-term, ‘learning-type’ elements of strategy update rules help cooperation in Prisoner's Dilemma games played on various networks. A low level of randomness (also called as ‘innovation’ in this paper) brings the level of cooperation closer in different network topologies.</p>", "links"=>[], "tags"=>["elements", "rules", "randomness", "stabilizes", "games", "played"], "article_id"=>603836, "categories"=>["Physics", "Biochemistry"], "users"=>["Shijun Wang", "Máté S. Szalay", "Changshui Zhang", "Peter Csermely"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0001917.g002", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Long_term_learning_elements_of_strategy_update_rules_help_while_a_low_level_of_randomness_relatively_stabilizes_cooperation_in_Prisoner_s_Dilemma_games_played_on_various_networks_/603836", "title"=>"Long-term learning elements of strategy update rules help, while a low level of randomness relatively stabilizes cooperation in Prisoner's Dilemma games played on various networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-09 01:03:56"}
• {"files"=>["https://ndownloader.figshare.com/files/460081"], "description"=>"<div><p>Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoner's Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules, when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the re-organization of real-world networks, and may play a prominent role in the evolution of self-organizing, complex systems.</p></div>", "links"=>[], "tags"=>["elements", "rules", "topologies"], "article_id"=>150655, "categories"=>["Physics", "Biochemistry"], "users"=>["Shijun Wang", "Máté S. Szalay", "Changshui Zhang", "Peter Csermely"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0001917", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Learning_and_Innovative_Elements_of_Strategy_Adoption_Rules_Expand_Cooperative_Network_Topologies/150655", "title"=>"Learning and Innovative Elements of Strategy Adoption Rules Expand Cooperative Network Topologies", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2008-04-09 00:10:55"}

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Relative Metric

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F1000Prime