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{"title"=>"How wealth accumulation can promote cooperation", "type"=>"journal", "authors"=>[{"first_name"=>"Thomas", "last_name"=>"Chadefaux", "scopus_author_id"=>"36620810700"}, {"first_name"=>"Dirk", "last_name"=>"Helbing", "scopus_author_id"=>"7005232363"}], "year"=>2010, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "pui"=>"359931320", "sgr"=>"78149428021", "doi"=>"10.1371/journal.pone.0013471", "scopus"=>"2-s2.0-78149428021", "isbn"=>"1932-6203", "pmid"=>"21048947"}, "id"=>"616aa698-75e4-3326-9056-2b3553898539", "abstract"=>"Explaining the emergence and stability of cooperation has been a central challenge in biology, economics and sociology. Unfortunately, the mechanisms known to promote it either require elaborate strategies or hold only under restrictive conditions. Here, we report the emergence, survival, and frequent domination of cooperation in a world characterized by selfishness and a strong temptation to defect, when individuals can accumulate wealth. In particular, we study games with local adaptation such as the prisoner's dilemma, to which we add heterogeneity in payoffs. In our model, agents accumulate wealth and invest some of it in their interactions. The larger the investment, the more can potentially be gained or lost, so that present gains affect future payoffs. We find that cooperation survives for a far wider range of parameters than without wealth accumulation and, even more strikingly, that it often dominates defection. This is in stark contrast to the traditional evolutionary prisoner's dilemma in particular, in which cooperation rarely survives and almost never thrives. With the inequality we introduce, on the contrary, cooperators do better than defectors, even without any strategic behavior or exogenously imposed strategies. These results have important consequences for our understanding of the type of social and economic arrangements that are optimal and efficient.", "link"=>"http://www.mendeley.com/research/wealth-accumulation-promote-cooperation", "reader_count"=>41, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Researcher"=>9, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>11, "Student > Postgraduate"=>2, "Student > Master"=>4, "Other"=>3, "Student > Bachelor"=>1, "Lecturer > Senior Lecturer"=>2, "Professor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Researcher"=>9, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>11, "Student > Postgraduate"=>2, "Student > Master"=>4, "Other"=>3, "Student > Bachelor"=>1, "Lecturer > Senior Lecturer"=>2, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>4, "Environmental Science"=>2, "Mathematics"=>1, "Agricultural and Biological Sciences"=>14, "Arts and Humanities"=>1, "Physics and Astronomy"=>4, "Social Sciences"=>6, "Computer Science"=>7}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Social Sciences"=>{"Social Sciences"=>6}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>14}, "Computer Science"=>{"Computer Science"=>7}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>2}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"Greece"=>1, "Romania"=>1, "United States"=>4, "Luxembourg"=>1, "China"=>1, "Philippines"=>1, "Brazil"=>1, "United Kingdom"=>1, "Portugal"=>2, "Switzerland"=>1}, "group_count"=>1}

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• http://doi.org/10.1209/0295-5075/94/30003
• http://doi.org/10.1103/PhysRevE.87.054801
• http://doi.org/10.1063/1.5120349
• http://doi.org/10.1371/journal.pone.0030902
• http://doi.org/10.1016/j.chaos.2018.08.029
• http://doi.org/10.1142/S0219525912500749
• http://doi.org/10.1016/j.tpb.2012.03.004
• http://doi.org/10.1016/j.physa.2017.10.034
• http://doi.org/10.1209/0295-5075/102/50006
• http://doi.org/10.1063/1.3613924
• http://doi.org/10.1007/s40844-019-00152-2
• http://doi.org/10.1371/journal.pone.0056016
• http://doi.org/10.1371/journal.pone.0121949
• http://doi.org/10.1038/srep32802
• http://doi.org/10.1086/669615

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Figshare

• {"files"=>["https://ndownloader.figshare.com/files/822360"], "description"=>"<p>The contour plots shows three different statistics as a function of the payoff parameters (horizontal axis) and (vertical axis), when the players' interaction network is of degree (‘Moore’ neighborhood). Panel A shows the final proportion of cooperators in the world (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g004\" target=\"_blank\">Figure 4</a>). Panel B shows the percentage of runs that end with more than 99% cooperators (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g006\" target=\"_blank\">Figure 6</a>). Panel C shows the percentage of runs in which at least 1% of cooperators survive after 1000 steps (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g005\" target=\"_blank\">Figure 5</a>). We note in particular that the results we obtained with the von-Neumann neighborhood hold under the Moore neighborhood, and even that the performance of cooperators is often improved as a result.</p>", "links"=>[], "tags"=>["cooperators", "accumulation", "moore"], "article_id"=>492739, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g010", "stats"=>{"downloads"=>4, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Asymptotic_proportion_domination_and_survival_of_cooperators_with_wealth_accumulation_under_the_Moore_neighborhood_/492739", "title"=>"Asymptotic proportion, domination, and survival of cooperators with wealth accumulation under the Moore neighborhood.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:42:27"}
• {"files"=>["https://ndownloader.figshare.com/files/821446"], "description"=>"<p>Snapshots of the lattice of a typical run (red denotes defectors, blue cooperators). (A) We start at with 50% cooperators. (B) After only a few steps (), the number of cooperators has dramatically decreased, and only a few cooperative clusters survive. (C) Those who do survive, however, expand () and (D) ultimately take over the entire lattice ().</p>", "links"=>[], "tags"=>["computer science", "Evolutionary biology", "mathematics/game theory"], "article_id"=>491819, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g001", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_cooperation_over_time_/491819", "title"=>"Evolution of cooperation over time.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:37:33"}
• {"files"=>["https://ndownloader.figshare.com/files/821576"], "description"=>"<p>The plot shows the evolution of the number of cooperators over a typical run (see also <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g001\" target=\"_blank\">Figure 1</a>), with (blue line) and without (red line) wealth accumulation. Initially, cooperators perform poorly. However, those cooperators who do survive the initial rounds have accumulated substantial amounts of wealth and are hence able to survive and spread. Over time, the proportion of cooperators converges to 1 (but typically does not reach it). The dashed lines represent two standard deviations.</p>", "links"=>[], "tags"=>["cooperators"], "article_id"=>491954, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g003", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_number_of_cooperators_over_time_/491954", "title"=>"Evolution of the number of cooperators over time.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:38:18"}
• {"files"=>["https://ndownloader.figshare.com/files/821867"], "description"=>"<p>The contour plot shows the percentage of runs that end with more than 99% cooperators, as a function of the payoff parameters (horizontal axis) and (vertical axis). In a world in which wealth is not accumulated (A), the range of parameters for which cooperation can take over is very limited (blue area in A). When the rich get richer (B), however, the range of parameters is far larger (blue area in B).</p>", "links"=>[], "tags"=>["computer science", "Evolutionary biology", "mathematics/game theory"], "article_id"=>492238, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g006", "stats"=>{"downloads"=>2, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Domination_of_cooperation_without_and_with_wealth_accumulation_/492238", "title"=>"<i>Domination</i> of cooperation without and with wealth accumulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:39:49"}
• {"files"=>["https://ndownloader.figshare.com/files/822219"], "description"=>"<p>Asymptotic proportion of cooperators as a function of the number of individuals. A larger number of individuals increases the likelihood that an initial supercritical cluster of cooperators will survive, and hence that at least one cooperator is protected sufficiently long to accumulate enough wealth to outcompete defectors. Hence, for any given set of parameters, a large number of individuals increases the probability with which cooperation will prevail.</p>", "links"=>[], "tags"=>["computer science", "Evolutionary biology", "mathematics/game theory"], "article_id"=>492594, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g009", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cooperation_as_a_function_of_the_number_of_individuals_/492594", "title"=>"Cooperation as a function of the number of individuals.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:41:40"}
• {"files"=>["https://ndownloader.figshare.com/files/822125"], "description"=>"<p>We tested the robustness of our results by using cumulative payoffs instead of the current step's payoff as the basis of adaptation. That is, agents here adapt to the strategy of their most successful neighbor, as measured by the total wealth they have accumulated over time, instead of the payoff they obtained in the previous step. Panel A shows the final proportion of cooperators in the world (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g004\" target=\"_blank\">Figure 4</a>). Panel B shows the percentage of runs that end with more than 99% cooperators (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g006\" target=\"_blank\">Figure 6</a>). Panel C shows the percentage of runs in which at least 1% of cooperators survive after 1000 steps (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g005\" target=\"_blank\">Figure 5</a>). Note that the results basically agree with the ones, when individuals imitate others based on their payoff in the previous time step, rather than their overall wealth, as is the case here (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g004\" target=\"_blank\">Figures 4B</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g005\" target=\"_blank\">5B</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone-0013471-g006\" target=\"_blank\">6B</a>).</p>", "links"=>[], "tags"=>["individuals", "imitate", "cumulative"], "article_id"=>492503, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g008", "stats"=>{"downloads"=>4, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Asymptotic_proportion_domination_and_survival_of_cooperators_when_individuals_imitate_others_based_on_cumulative_wealth_/492503", "title"=>"Asymptotic proportion, domination, and survival of cooperators, when individuals imitate others based on cumulative wealth.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:41:12"}
• {"files"=>["https://ndownloader.figshare.com/files/821679"], "description"=>"<p>The contour plot shows the average final proportion of cooperators in the world, as a function of the payoff parameters (horizontal axis) and (vertical axis). (A) In a world in which payoffs are homogenous across agents, the proportion of cooperators is low for any . (B) In an unequal environment, in which the rich can become richer, cooperation is stable for a much larger range of payoff parameters. The top-left quadrant corresponds to the harmony game (HG); the bottom-left ( and ) to the stag-hunt (or ‘assurance’) game (SH); the upper-right quadrant (, ) to the snowdrift (or ‘chicken’) game (SD); and the lower-right quadrant ( and ) corresponds to the prisoner's dilemma (PD) <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0013471#pone.0013471-Roca1\" target=\"_blank\">[33]</a>.</p>", "links"=>[], "tags"=>["cooperators"], "article_id"=>492056, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g004", "stats"=>{"downloads"=>5, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Asymptotic_proportion_of_cooperators_without_and_with_wealth_accumulation_/492056", "title"=>"Asymptotic <i>proportion</i> of cooperators without and with wealth accumulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:38:52"}
• {"files"=>["https://ndownloader.figshare.com/files/821936"], "description"=>"<p>This plot shows the impact of the multiplier (see eqn. 1) on the final average proportion of cooperators in the world, for typical parameter values.</p>", "links"=>[], "tags"=>["cooperators"], "article_id"=>492314, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g007", "stats"=>{"downloads"=>4, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Final_proportion_of_cooperators_as_a_function_of_/492314", "title"=>"Final proportion of cooperators as a function of .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:40:12"}
• {"files"=>["https://ndownloader.figshare.com/files/821779"], "description"=>"<p>The contour plot shows the percentage of runs in which at least 1% of cooperators survive after 1000 steps, as a function of the payoff parameters (horizontal axis) and (vertical axis). Note that cooperation can survive in much more hostile conditions ( and ) when payoffs are unequal (panel B) than when they are not (panel A). In particular, for extreme values ( close to 2 and close to −1), cooperation never survives without wealth accumulation, but can survive with it.</p>", "links"=>[], "tags"=>["computer science", "Evolutionary biology", "mathematics/game theory"], "article_id"=>492156, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g005", "stats"=>{"downloads"=>4, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Survival_of_cooperation_without_and_with_wealth_accumulation_/492156", "title"=>"<i>Survival</i> of cooperation without and with wealth accumulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:39:23"}
• {"files"=>["https://ndownloader.figshare.com/files/821519"], "description"=>"<p>The plot measures inequality by reporting the evolution over time of the population's Gini coefficient. We use the players' cumulative wealth to calculate the coefficient. Because of the setup in which we allow the rich to become increasingly rich, the coefficient rapidly reaches extreme levels, implying that wealth ends up being very unevenly distributed among individuals, with only a few owning most of the total accumulated wealth.</p>", "links"=>[], "tags"=>["coefficient"], "article_id"=>491898, "categories"=>["Information And Computing Sciences", "Mathematics", "Evolutionary Biology"], "users"=>["Thomas Chadefaux", "Dirk Helbing"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0013471.g002", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Gini_coefficient_over_time_in_a_typical_run_/491898", "title"=>"Gini coefficient over time in a typical run.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 22:38:01"}

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Relative Metric

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F1000Prime