The evolution of cooperation and diversity by integrated indirect reciprocity

Indirect reciprocity is one of the major mechanisms for the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream. Cooperation in downstream reciprocity follows the pattern, 'You helped someone, and I will help you'. The direction of cooperation is reversed in upstream reciprocity, which instead follows the pattern, 'You helped me, and I will help someone else'. In reality, these two types of indirect reciprocity often occur in combination. However, upstream and downstream reciprocity have mostly been studied theoretically in isolation. Here, we propose a new model that integrates both types. We apply the standard giving-game framework of indirect reciprocity and analyze the model by means of evolutionary game theory. We show that the model can result in the stable coexistence of altruistic reciprocators and free riders in well-mixed populations. We also found that considering inattention in the assessment rule can strengthen the stability of this mixed equilibrium, even resulting in a global attractor. Our results indicate that the cycles of forwarding help and rewarding help need to be established for creating and maintaining diversity and inclusion in a society.

[1]  C. Hauert,et al.  Spatial social dilemmas promote diversity , 2021, Proceedings of the National Academy of Sciences.

[2]  Simone Righi,et al.  Reputation and punishment sustain cooperation in the optional public goods game , 2021, Philosophical Transactions of the Royal Society B.

[3]  Ali Seyhun Saral,et al.  Direct and indirect reciprocity among individuals and groups. , 2021, Current opinion in psychology.

[4]  M. Nowak,et al.  A unified framework of direct and indirect reciprocity , 2021, Nature Human Behaviour.

[5]  Caitlin C. Ferreira,et al.  Who pays it forward the most? Examining organizational citizenship behavior in the workplace , 2020, Journal of Theoretical Social Psychology.

[6]  Isamu Okada,et al.  A Review of Theoretical Studies on Indirect Reciprocity , 2020, Games.

[7]  Takahisa Suzuki,et al.  Justified defection is neither justified nor unjustified in indirect reciprocity , 2020, PloS one.

[8]  Brent Simpson,et al.  The robustness of reciprocity: Experimental evidence that each form of reciprocity is robust to the presence of other forms of reciprocity , 2020, Science Advances.

[9]  Ji Eun Kim,et al.  Cheating in online gaming spreads through observation and victimization , 2020, Network Science.

[10]  Chia-huei Wu,et al.  Generalized exchange orientation: Conceptualization and scale development. , 2020, The Journal of applied psychology.

[11]  Krishnendu Chatterjee,et al.  Indirect reciprocity with private, noisy, and incomplete information , 2018, Proceedings of the National Academy of Sciences.

[12]  Hitoshi Yamamoto,et al.  Experimental evidence of selective inattention in reputation-based cooperation , 2018, Scientific Reports.

[13]  Tatsuya Sasaki,et al.  A solution for private assessment in indirect reciprocity using solitary observation. , 2018, Journal of theoretical biology.

[14]  Francisco C. Santos,et al.  Social norm complexity and past reputations in the evolution of cooperation , 2018, Nature.

[15]  Tatsuya Sasaki,et al.  A Theoretical Approach to Norm Ecosystems: Two Adaptive Architectures of Indirect Reciprocity Show Different Paths to the Evolution of Cooperation , 2018, Front. Phys..

[16]  David G. Rand,et al.  Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness , 2018, Nature Communications.

[17]  Brent Simpson,et al.  The Roots of Reciprocity: Gratitude and Reputation in Generalized Exchange Systems , 2018 .

[18]  Y. Nakai,et al.  Tolerant indirect reciprocity can boost social welfare through solidarity with unconditional cooperators in private monitoring , 2017, Scientific Reports.

[19]  Tatsuya Sasaki,et al.  A norm knockout method on indirect reciprocity to reveal indispensable norms , 2017, Scientific Reports.

[20]  Tatsuya Sasaki,et al.  The evolution of conditional moral assessment in indirect reciprocity , 2016, Scientific Reports.

[21]  Wayne E. Baker,et al.  Paying It Forward versus Rewarding Reputation: Mechanisms of Generalized Reciprocity , 2014, Organ. Sci..

[22]  Michael W. Macy,et al.  The Social Contagion of Generosity , 2014, PloS one.

[23]  Martin A. Nowak,et al.  Powering up with indirect reciprocity in a large-scale field experiment , 2013, Proceedings of the National Academy of Sciences.

[24]  Luis A. Martinez-Vaquero,et al.  Evolutionary stability and resistance to cheating in an indirect reciprocity model based on reputation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  W. Press,et al.  Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent , 2012, Proceedings of the National Academy of Sciences.

[26]  Ulrich Berger,et al.  Learning to cooperate via indirect reciprocity , 2011, Games Econ. Behav..

[27]  István Scheuring,et al.  COEXISTENCE OF COOPERATION AND DEFECTION IN PUBLIC GOODS GAMES , 2011, Evolution; international journal of organic evolution.

[28]  Satoshi Uchida,et al.  Effect of private information on indirect reciprocity. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  David DeSteno,et al.  Gratitude as moral sentiment: emotion-guided cooperation in economic exchange. , 2010, Emotion.

[30]  Karl Sigmund,et al.  The competition of assessment rules for indirect reciprocity. , 2010, Journal of theoretical biology.

[31]  Nicholas A. Christakis,et al.  Cooperative behavior cascades in human social networks , 2009, Proceedings of the National Academy of Sciences.

[32]  Daniel J. Rankin,et al.  Assortment and the Evolution of Generalized Reciprocity , 2009, Evolution; international journal of organic evolution.

[33]  L. Stanca.  Measuring Indirect Reciprocity: Whose Back Do We Scratch? , 2009 .

[34]  Martin A. Nowak,et al.  Indirect reciprocity provides a narrow margin of efficiency for costly punishment , 2008, Nature.

[35]  Robb Willer,et al.  Altruism and Indirect Reciprocity: The Interaction of Person and Situation in Prosocial Behavior , 2008 .

[36]  M. Taborsky,et al.  Generalized Reciprocity in Rats , 2007, PLoS biology.

[37]  Sébastien Roch,et al.  Upstream reciprocity and the evolution of gratitude , 2007, Proceedings of the Royal Society B: Biological Sciences.

[38]  Yoh Iwasa,et al.  Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation. , 2007, Journal of theoretical biology.

[39]  Nobuyuki Takahashi,et al.  The importance of subjectivity in perceptual errors on the emergence of indirect reciprocity. , 2006, Journal of theoretical biology.

[40]  Yoh Iwasa,et al.  The leading eight: social norms that can maintain cooperation by indirect reciprocity. , 2006, Journal of theoretical biology.

[41]  Karl Sigmund,et al.  The good, the bad and the discriminator--errors in direct and indirect reciprocity. , 2006, Journal of theoretical biology.

[42]  Sebastian Bonhoeffer,et al.  Evolution of cooperation by generalized reciprocity , 2005, Proceedings of the Royal Society B: Biological Sciences.

[43]  Karl Sigmund,et al.  Indirect reciprocity, image scoring, and moral hazard. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[44]  Karl Sigmund,et al.  The logic of reprobation: assessment and action rules for indirect reciprocation. , 2004, Journal of theoretical biology.

[45]  Yoh Iwasa,et al.  How should we define goodness?--reputation dynamics in indirect reciprocity. , 2004, Journal of theoretical biology.

[46]  C. Hauert,et al.  The Evolutionary Origin of Cooperators and Defectors , 2004, Science.

[47]  Michael A Fishman,et al.  Indirect reciprocity among imperfect individuals. , 2003, Journal of theoretical biology.

[48]  Karthik Panchanathan,et al.  A tale of two defectors: the importance of standing for evolution of indirect reciprocity. , 2003, Journal of theoretical biology.

[49]  Lik Mui,et al.  Evolution of indirect reciprocity by social information: the role of trust and reputation in evolution of altruism. , 2003, Journal of theoretical biology.

[50]  B. Malinowski.  Argonauts of the Western Pacific: An Account of Native Enterprise and Adventure in the Archipelagoes of Melanesian New Guinea , 2002 .

[51]  M. Milinski,et al.  Reputation helps solve the ‘tragedy of the commons’ , 2002, Nature.

[52]  O. Leimar,et al.  Evolution of cooperation through indirect reciprocity , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[53]  Arnon Lotem,et al.  Evolution of cooperation between individuals , 1999, Nature.

[54]  M. Nowak,et al.  Evolution of indirect reciprocity by image scoring , 1998, Nature.

[55]  Karen S. Cook,et al.  Generalized Exchange and Social Dilemmas , 1993 .

[56]  E. Uehara,et al.  Dual Exchange Theory, Social Networks, and Informal Social Support , 1990, American Journal of Sociology.

[57]  P. Richerson,et al.  The evolution of indirect reciprocity , 1989 .

[58]  R. D. Alexander,et al.  The biology of moral systems , 1989 .

[59]  W. Hamilton,et al.  The evolution of cooperation. , 1984, Science.

[60]  R. Trivers.  The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

[61]  Adrian F. Ward,et al.  Paying it forward: generalized reciprocity and the limits of generosity. , 2014, Journal of experimental psychology. General.

[62]  Manfred Milinski,et al.  The Calculus of Selfishness , 2011 .

[63]  M. N,et al.  The Dynamics of Indirect Reciprocity , 1998 .

[64]  Michihiro Kandori.  Social Norms and Community Enforcement , 1992 .

[65]  R. Sugden.  The Economics of Rights, Co-Operation, and Welfare , 1986 .