O ct 2 02 1 The strength of diversity

Can one demonstrate quantitative effects of diversity within a system comprised of distinct individuals on the performance of the system as a whole? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level ramifications. Rooted in theoretical mathematics, the model is not constrained to any specific context. Potential applications include research, education, sports, politics, ecology, agriculture, algorithms, and finance. 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 with others. The second main contribution is the rigorous identification of all equilibrium points and strategies. 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 with others.

[1]  T. Rynearson,et al.  Biodiversity of marine microbes is safeguarded by phenotypic heterogeneity in ecological traits , 2020, PloS one.

[2]  C. Fine,et al.  Why Does Workplace Gender Diversity Matter? Justice, Organizational Benefits, and Policy , 2019, Social Issues and Policy Review.

[3]  T. Chou,et al.  Diversity in biology: definitions, quantification and models , 2019, Physical biology.

[4]  Joseph Simonian.  Portfolio Selection: A Game-Theoretic Approach , 2019, The Journal of Portfolio Management.

[5]  Tobias Hiller.  Structure of teams—A cooperative game theory approach , 2019, Managerial and Decision Economics.

[6]  Sung Yong Park,et al.  CCMP: Software-as-a-service approach for fully-automated microbiome profiling , 2019, J. Biomed. Informatics X.

[7]  Talal Rahwan,et al.  The preeminence of ethnic diversity in scientific collaboration , 2018, Nature Communications.

[8]  D. Tilman,et al.  Sustainable intensification of high-diversity biomass production for optimal biofuel benefits , 2018, Nature Sustainability.

[9]  A. Godhe,et al.  High single‐cell diversity in carbon and nitrogen assimilations by a chain‐forming diatom across a century , 2018, Environmental microbiology.

[10]  Emily A. Martin,et al.  Landscape‐level crop diversity benefits biological pest control , 2018 .

[11]  J. Rowlett,et al.  The theory of games and microbe ecology , 2018, Theoretical Ecology.

[12]  George B. Cunningham,et al.  Group diversity's influence on sport teams and organizations: a meta-analytic examination and identification of key moderators , 2018, European Sport Management Quarterly.

[13]  Dirk Sudholt,et al.  The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses , 2018, Theory of Evolutionary Computation.

[14]  C. Hoppe,et al.  Resilience by diversity: Large intraspecific differences in climate change responses of an Arctic diatom , 2018 .

[15]  M. Wooders,et al.  Non-Cooperative Team Formation and a Team Formation Mechanism , 2017 .

[16]  A. Godhe,et al.  The role of intraspecific variation in the ecological and evolutionary success of diatoms in changing environments , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[17]  K. Kimmel,et al.  Benefits of increasing plant diversity in sustainable agroecosystems , 2017 .

[18]  Visa Koivunen,et al.  Coalitional Game-Based Cost Optimization of Energy Portfolio in Smart Grid Communities , 2017, IEEE Transactions on Smart Grid.

[19]  G. Barabás,et al.  The effect of intraspecific variation and heritability on community pattern and robustness. , 2016, Ecology letters.

[20]  Sripad K. Devalkar,et al.  Crop diversification and risk management in Indian agriculture , 2016 .

[21]  Y. Kimura,et al.  A bacterium that degrades and assimilates poly(ethylene terephthalate) , 2016, Science.

[22]  T. Rynearson,et al.  Persistent Intra-Specific Variation in Genetic and Behavioral Traits in the Raphidophyte, Heterosigma akashiwo , 2015, Front. Microbiol..

[23]  M. Saito,et al.  Co-occurring Synechococcus ecotypes occupy four major oceanic regimes defined by temperature, macronutrients and iron , 2015, The ISME Journal.

[24]  S. Menden‐Deuer,et al.  Bloom formation potential in the harmful dinoflagellate Akashiwo sanguinea: Clues from movement behaviors and growth characteristics , 2015 .

[25]  Luis Pedro Coelho,et al.  Structure and function of the global ocean microbiome , 2015, Science.

[26]  P. Bork,et al.  Eukaryotic plankton diversity in the sunlit ocean , 2015, Science.

[27]  S. Giovannoni,et al.  Rethinking the marine carbon cycle: Factoring in the multifarious lifestyles of microbes , 2015, Science.

[28]  A. Calabrò,et al.  Board of Directors’ Diversity, Creativity, and Cognitive Conflict , 2015 .

[29]  V. Young,et al.  The gut microbiome in health and in disease , 2015, Current opinion in gastroenterology.

[30]  Vladimir V. Mazalov,et al.  Mathematical Game Theory and Applications , 2014 .

[31]  J. Rowlett,et al.  Many ways to stay in the game: individual variability maintains high biodiversity in planktonic microorganisms , 2014, Journal of The Royal Society Interface.

[32]  Jing Jiang,et al.  Crop Diversification in Coping with Extreme Weather Events in China , 2014 .

[33]  N. Kashtan,et al.  Single-Cell Genomics Reveals Hundreds of Coexisting Subpopulations in Wild Prochlorococcus , 2014, Science.

[34]  Elena Litchman,et al.  Marine Phytoplankton Temperature versus Growth Responses from Polar to Tropical Waters – Outcome of a Scientific Community-Wide Study , 2013, PloS one.

[35]  A. Millar,et al.  Variation in plastic responses of a globally distributed picoplankton species to ocean acidification , 2013 .

[36]  Yang Xiao,et al.  Game Theory for Network Security , 2013, IEEE Communications Surveys & Tutorials.

[37]  M. Nivet.  Commentary: Diversity 3.0: a necessary systems upgrade. , 2011, Academic medicine : journal of the Association of American Medical Colleges.

[38]  George B. Cunningham,et al.  The Benefits of Sexual Orientation Diversity in Sport Organizations , 2011, Journal of homosexuality.

[39]  Yang Yang,et al.  Multi-Portfolio Optimization: A Potential Game Approach , 2011, IEEE Transactions on Signal Processing.

[40]  B. Lin.  Resilience in Agriculture through Crop Diversification: Adaptive Management for Environmental Change , 2011 .

[41]  R. Dick,et al.  Recognizing the benefits of diversity: When and how does diversity increase group performance? , 2010 .

[42]  Francisco Sánchez-Sánchez,et al.  Rankings and values for team games , 2010, Int. J. Game Theory.

[43]  Tansu Alpcan,et al.  Coalitional Game Theory for Security Risk Management , 2010, 2010 Fifth International Conference on Internet Monitoring and Protection.

[44]  George Leitmann,et al.  A Differential Game Related to Terrorism: Nash and Stackelberg Strategies , 2010 .

[45]  Johannes K. Chiang,et al.  Decision making model on strategic technology investment using game theory , 2009, 2009 IEEE International Conference on Industrial Engineering and Engineering Management.

[46]  Khashayar Khorasani,et al.  Multi-agent team cooperation: A game theory approach , 2009, Autom..

[47]  S. Voelpel,et al.  WHEN AND HOW DIVERSITY BENEFITS TEAMS: THE IMPORTANCE OF TEAM MEMBERS' NEED FOR COGNITION , 2009 .

[48]  E. Delong,et al.  The Microbial Engines That Drive Earth's Biogeochemical Cycles , 2008, Science.

[49]  William R. Kerr,et al.  Ethnic Scientific Communities and International Technology Diffusion , 2007, The Review of Economics and Statistics.

[50]  J. Bohman,et al.  Deliberative Democracy and the Epistemic Benefits of Diversity , 2006, Episteme.

[51]  Sallie W. Chisholm,et al.  Niche Partitioning Among Prochlorococcus Ecotypes Along Ocean-Scale Environmental Gradients , 2006, Science.

[52]  S. Chisholm,et al.  Measurement of Prochlorococcus ecotypes using real-time polymerase chain reaction reveals different abundances of genotypes with similar light physiologies. , 2006, Environmental microbiology.

[53]  Jeannette M. Wing,et al.  Game strategies in network security , 2005, International Journal of Information Security.

[54]  Barry Smit,et al.  Farm-Level Adaptation to Climatic Variability and Change: Crop Diversification in the Canadian Prairies , 2004 .

[55]  G. Gambarelli,et al.  Takeover prices and portfolio theory , 2004 .

[56]  Jeffrey F. Milem.  Chapter Five THE EDUCATIONAL BENEFITS OF DIVERSITY: EVIDENCE FROM MULTIPLE SECTORS , 2003, Compelling Interest.

[57]  M. Feldman,et al.  Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors , 2002, Nature.

[58]  Elena Litchman,et al.  Algal games: The vertical distribution of phytoplankton in poorly mixed water columns , 2001 .

[59]  Daryl G. Smith,et al.  The Benefits of Diversity what the Research Tells Us , 2000 .

[60]  J. P. Grime,et al.  Benefits of plant diversity to ecosystems: immediate, filter and founder effects , 1998 .

[61]  Byung Ha Lim,et al.  A Minimax Portfolio Selection Rule with Linear Programming Solution , 1998 .

[62]  Shmuel Zamir,et al.  Cooperation in Intergroup, N-Person, and Two-Person Games of Chicken , 1997 .

[63]  T. Cover,et al.  Game-theoretic optimal portfolios , 1988 .

[64]  Peter Hammerstein,et al.  Game Theory in the Ecological Context , 1983 .

[65]  Robert M. May,et al.  The evolution of cooperation , 1981, Science.

[66]  Y. Amihud,et al.  Portfolio selection for managerial control , 1974 .

[67]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[68]  G. Hunanyan,et al.  Portfolio Selection , 2019, Finanzwirtschaft, Banken und Bankmanagement I Finance, Banks and Bank Management.

[69]  Jing Fu,et al.  Information Pooling Game in Multi-Portfolio Optimization , 2017 .

[70]  Jonas Schmitt.  Portfolio Selection Efficient Diversification Of Investments , 2016 .

[71]  R. Zhao,et al.  Analysis of Environmental Governance for Construction Project Based on a Dynamic Non-cooperative Game , 2013 .

[72]  L. Poorter,et al.  Inaugural Article: Linking functional diversity and social actor strategies in a framework for interdisciplinary analysis of nature's benefits to society , 2011 .

[73]  Jorma Jormakka,et al.  Modelling Information Warfare as a Game , 2005 .

[74]  M. Simaan,et al.  Noninferior Nash Strategies for Multi-Team Systems , 2004 .

[75]  J. Reif,et al.  On Multiplayer Non-Cooperative Games of Incomplete Information: Part 2 - Lower Bounds , 1991 .