The Effect of Incentives and Meta-incentives on the Evolution of Cooperation
Publication Date
May 14, 2015
Journal
PLOS Computational Biology
Authors
Isamu Okada, Hitoshi Yamamoto, Fujio Toriumi & Tatsuya Sasaki
Volume
11
Issue
5
Pages
e1004232
DOI
https://dx.plos.org/10.1371/journal.pcbi.1004232
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1004232
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/25974684
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4431686
Europe PMC
http://europepmc.org/abstract/MED/25974684
Web of Science
000356700200020
Scopus
84930603861
Mendeley
http://www.mendeley.com/research/effect-incentives-metaincentives-evolution-cooperation
Events
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Mendeley | Further Information

{"title"=>"The Effect of Incentives and Meta-incentives on the Evolution of Cooperation", "type"=>"journal", "authors"=>[{"first_name"=>"Isamu", "last_name"=>"Okada", "scopus_author_id"=>"7005931788"}, {"first_name"=>"Hitoshi", "last_name"=>"Yamamoto", "scopus_author_id"=>"55725331000"}, {"first_name"=>"Fujio", "last_name"=>"Toriumi", "scopus_author_id"=>"22836892600"}, {"first_name"=>"Tatsuya", "last_name"=>"Sasaki", "scopus_author_id"=>"54933570700"}], "year"=>2015, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"84930603861", "doi"=>"10.1371/journal.pcbi.1004232", "pui"=>"604784527", "pmid"=>"25974684", "scopus"=>"2-s2.0-84930603861", "issn"=>"15537358"}, "id"=>"bacf2f30-f9bd-3fc5-9418-07a6adcf3411", "abstract"=>"Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players' incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.", "link"=>"http://www.mendeley.com/research/effect-incentives-metaincentives-evolution-cooperation", "reader_count"=>25, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>4, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>6, "Student > Master"=>4, "Student > Bachelor"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>4, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>6, "Student > Master"=>4, "Student > Bachelor"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Unspecified"=>2, "Mathematics"=>1, "Agricultural and Biological Sciences"=>3, "Philosophy"=>1, "Arts and Humanities"=>1, "Business, Management and Accounting"=>1, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Physics and Astronomy"=>2, "Psychology"=>2, "Social Sciences"=>5, "Computer Science"=>4, "Economics, Econometrics and Finance"=>2}, "reader_count_by_subdiscipline"=>{"Social Sciences"=>{"Social Sciences"=>5}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Psychology"=>{"Psychology"=>2}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>3}, "Computer Science"=>{"Computer Science"=>4}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>2}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "United States"=>1, "Japan"=>1}, "group_count"=>0}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2067668"], "description"=>"<p>The triangle represents the state space, Δ = {(<i>x</i>, <i>y</i>, <i>z</i>)*** : <i>x</i>, <i>y</i>, <i>z</i> ≥ 0, <i>x</i>+<i>y</i>+<i>z</i> = 1}, where <i>x</i>, <i>y</i>, and <i>z</i> are respectively the frequencies of the cooperative incentive-providers, cooperative incentive-non-providers, and non-cooperative incentive-non-providers. </p><p></p><p><mo stretchy=\"false\">(</mo><mi>μ</mi><mo>,</mo><mi>δ</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo stretchy=\"false\">(</mo><mn>3</mn><mo>,</mo></p><p><mn>1</mn><mn>2</mn></p><mo stretchy=\"false\">)</mo><p></p><p></p>. (A) PR+R, (B) PP, (C) PB+RB(Full), and (D) RB. The abbreviations are defined in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.t001\" target=\"_blank\">Table 1</a>. In (A), (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0) is unstable, so cooperation is never achieved regardless of the values of (<i>μ</i>, <i>δ</i>). In (B), the whole line <i>z</i> = 0 consists of fixed points, and thus, neutral drift is possible. In (C) and (D), (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0) is a locally asymptotically stable point depending on the values of (<i>μ</i>, <i>δ</i>), and thus, a cooperative regime can emerge. In (C), the unstable equilibrium in the internal part on <i>z</i> = 0, <i>K</i><sub><i>z</i></sub>, is a saddle, and that on <i>y</i> = 0, <i>K</i><sub><i>y</i></sub>, is a source. In (D), <i>K</i><sub><i>z</i></sub> is a source, while <i>K</i><sub><i>y</i></sub> is a saddle.<p></p>", "links"=>[], "tags"=>["game types", "replicator dynamics", "proactive system", "donation games", "incentive behaviors"], "article_id"=>1414733, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Isamu Okada", "Hitoshi Yamamoto", "Fujio Toriumi", "Tatsuya Sasaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004232.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Replicator_dynamics_analysis_of_representative_S_MIGs_on_2_dimensional_simplex_/1414733", "title"=>"Replicator dynamics analysis of representative S-MIGs on 2-dimensional simplex.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-14 02:46:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/2067663"], "description"=>"<p>Four individuals are randomly drawn from the population and randomly assigned to one of four roles, recipient, donor, first-order player, and second-order player. In the first stage, the donor decides whether to help the recipient. In the second stage, the first-order player decides whether to provide an incentive for the donor; and in the last stage, the second-order player decides whether to provide an incentive to the first-order player.</p>", "links"=>[], "tags"=>["game types", "replicator dynamics", "proactive system", "donation games", "incentive behaviors"], "article_id"=>1414728, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Isamu Okada", "Hitoshi Yamamoto", "Fujio Toriumi", "Tatsuya Sasaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004232.g001", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_meta_incentive_game_MIG_/1414728", "title"=>"Illustration of meta-incentive game (MIG).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-14 02:46:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/2067670"], "description"=>"<p></p><p></p><p></p><p><mi>x</mi><mo>.</mo></p><p></p><p></p> functions on the lines <i>y</i> = 0 and <i>z</i> = 0 for each type of S-MIG. Here, <i>f</i>(<i>x</i>) and <i>g</i>(<i>x</i>) are defined in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.e016\" target=\"_blank\">Eq (5)</a>.<p></p>", "links"=>[], "tags"=>["game types", "replicator dynamics", "proactive system", "donation games", "incentive behaviors"], "article_id"=>1414735, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Isamu Okada", "Hitoshi Yamamoto", "Fujio Toriumi", "Tatsuya Sasaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004232.t002", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_x_functions_on_the_lines_y_0_and_z_0_for_each_type_of_S_MIG_Here_f_x_and_g_x_are_defined_in_Eq_5_/1414735", "title"=>"x. functions on the lines <i>y</i> = 0 and <i>z</i> = 0 for each type of S-MIG. Here, <i>f</i>(<i>x</i>) and <i>g</i>(<i>x</i>) are defined in Eq (5).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-05-14 02:46:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/2067671"], "description"=>"<p>Equations and solutions of <i>z</i>* in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.e060\" target=\"_blank\">Eq (6)</a> for each type.</p>", "links"=>[], "tags"=>["game types", "replicator dynamics", "proactive system", "donation games", "incentive behaviors"], "article_id"=>1414736, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Isamu Okada", "Hitoshi Yamamoto", "Fujio Toriumi", "Tatsuya Sasaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004232.t003", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Equations_and_solutions_of_z_in_Eq_6_for_each_type_/1414736", "title"=>"Equations and solutions of <i>z</i>* in Eq (6) for each type.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-05-14 02:46:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/2067669"], "description"=>"<p>Types of MIG.</p>", "links"=>[], "tags"=>["game types", "replicator dynamics", "proactive system", "donation games", "incentive behaviors"], "article_id"=>1414734, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Isamu Okada", "Hitoshi Yamamoto", "Fujio Toriumi", "Tatsuya Sasaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004232.t001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Types_of_MIG_/1414734", "title"=>"Types of MIG.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-05-14 02:46:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/2067665"], "description"=>"<p>This figure illustrates all 24 types of S-MIG. The abbreviations are defined in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.t001\" target=\"_blank\">Table 1</a>. Their vertical layering in the figure reflects the existence condition for the basin of attraction on the point (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0) related to (<i>μ</i>, <i>δ</i>) under which a cooperative regime emerges. The frames represent the form of local stability at point (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0): the point is unstable for each type in the top frame which corresponds to (A) in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.g003\" target=\"_blank\">Fig 3</a>, is a non-isolated equilibrium for each type in the bottom right frame which corresponds to (B) in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.g003\" target=\"_blank\">Fig 3</a>, and is asymptotically stable for each type in the bottom left frame which corresponds to (C) and (D) in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.g003\" target=\"_blank\">Fig 3</a>.</p>", "links"=>[], "tags"=>["game types", "replicator dynamics", "proactive system", "donation games", "incentive behaviors"], "article_id"=>1414730, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Isamu Okada", "Hitoshi Yamamoto", "Fujio Toriumi", "Tatsuya Sasaki"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1004232.g002", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_replicator_dynamics_analyses_for_each_type_of_S_MIG_/1414730", "title"=>"Illustration of replicator dynamics analyses for each type of S-MIG.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-14 02:46:46"}

PMC Usage Stats | Further Information

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  • {"unique-ip"=>"9", "full-text"=>"7", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"3"}
  • {"unique-ip"=>"12", "full-text"=>"13", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"4"}
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  • {"unique-ip"=>"7", "full-text"=>"7", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"6"}
  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"7"}
  • {"unique-ip"=>"7", "full-text"=>"7", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"9"}
  • {"unique-ip"=>"8", "full-text"=>"9", "pdf"=>"6", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"10"}

Relative Metric

{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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