Rewards based on public loyalty program promote cooperation in public goods game

Abstract The loyalty program (LP) is a marketing campaign designed to encourage customer loyalty by rewarding them. Motivated by extensively applied LP in real society, we propose a public loyalty program (PLP) in the public goods game (PGG). In the PLP, players are rewarded differentially depending on whether their cumulative contribution exceeds the reward threshold. The progressive accumulation rate scheme (PAR) rewards player for increasing accumulation rate (points obtained per unit contribution), while the progressive redemption rate scheme (PRR) increases the redemption rate (subsidy obtained per unit point). By means of theoretical and numerical analyses, we find that PAR can promote cooperation, but the effect is not significant. In the PRR, the combination of a small base redemption rate and a large progressive redemption rate achieves the highest level of cooperation at the medium reward threshold. The introduction of PLP in the PGG fosters and rewards the behavior and attitude loyalty of participants. While reducing cost pressure, it has reshaped the long-term bilateral relationship between the government and the public.

[1]  G. Szabo,et al.  Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks , 2008, 0802.2807.

[2]  Juan Wang,et al.  Inferring the reputation enhances the cooperation in the public goods game on interdependent lattices , 2017, Appl. Math. Comput..

[3]  Matjaz Perc,et al.  Does strong heterogeneity promote cooperation by group interactions? , 2011, ArXiv.

[4]  Yuping Liu.  The Long-Term Impact of Loyalty Programs on Consumer Purchase Behavior and Loyalty , 2007 .

[5]  Mouez Fodha,et al.  From regressive pollution taxes to progressive environmental tax reforms , 2014 .

[6]  Qiang Wang,et al.  Replicator dynamics for public goods game with resource allocation in large populations , 2018, Appl. Math. Comput..

[7]  Tammo H. A. Bijmolt,et al.  Loyalty Programmes: Current Knowledge and Research Directions , 2012 .

[8]  Isamu Okada,et al.  How to keep punishment to maintain cooperation: Introducing social vaccine , 2016 .

[9]  Miguel dos Santos.  The evolution of anti-social rewarding and its countermeasures in public goods games , 2015 .

[10]  Yannis M. Ioannides,et al.  Neighborhood Effects: Accomplishments and Looking Beyond Them , 2010 .

[11]  Attila Szolnoki,et al.  Punishment and inspection for governing the commons in a feedback-evolving game , 2018, PLoS Comput. Biol..

[12]  Yongjie Wang,et al.  Cleverly handling the donation information can promote cooperation in public goods game , 2019, Appl. Math. Comput..

[13]  C. Hauert,et al.  Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games , 2002, Science.

[14]  Praveen K. Kopalle,et al.  The Joint Sales Impact of Frequency Reward and Customer Tier Components of Loyalty Programs , 2012, Mark. Sci..

[15]  Hsiao-chien Tsui.  What affects happiness: Absolute income, relative income or expected income? , 2014 .

[16]  Jun Tanimoto.  The effect of assortativity by degree on emerging cooperation in a 2×2 dilemma game played on an evolutionary network , 2010 .

[17]  Jun Tanimoto,et al.  Difference of reciprocity effect in two coevolutionary models of presumed two-player and multiplayer games. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Juan Wang,et al.  Promotion of cooperation due to diversity of players in the spatial public goods game with increasing neighborhood size , 2014 .

[19]  E. Breugelmans,et al.  The Impact of an Item-Based Loyalty Program on Consumer Purchase Behavior , 2012 .

[20]  Eric K. Foster.  Research on Gossip: Taxonomy, Methods, and Future Directions , 2004 .

[21]  Andrew Smith,et al.  "It's nice to get a wee treat if you've had a bad week": Consumer motivations in retail loyalty scheme points redemption , 2009 .

[22]  Attila Szolnoki,et al.  Central governance based on monitoring and reporting solves the collective-risk social dilemma , 2018, Appl. Math. Comput..

[23]  Tatsuya Sasaki,et al.  Rewards and the evolution of cooperation in public good games , 2013, Biology Letters.

[24]  Lin Wang,et al.  Evolutionary games on multilayer networks: a colloquium , 2015, The European Physical Journal B.

[25]  Attila Szolnoki,et al.  Rewarding evolutionary fitness with links between populations promotes cooperation , 2014, Journal of theoretical biology.

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

[27]  Thilo Gross,et al.  Consequences of fluctuating group size for the evolution of cooperation , 2010, Journal of mathematical biology.

[28]  Bettina Rockenbach,et al.  Human behaviour: Punisher pays , 2008, Nature.

[29]  W. David Pierce,et al.  Positive Effects of Rewards and Performance Standards on Intrinsic Motivation , 2003 .

[30]  M. Milinski,et al.  Volunteering leads to rock–paper–scissors dynamics in a public goods game , 2003, Nature.

[31]  M. Perc,et al.  Group-Size Effects on the Evolution of Cooperation in the Spatial Public Goods Game , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Attila Szolnoki,et al.  Evolutionary advantages of adaptive rewarding , 2012, 1208.3457.

[33]  Lei Zhang,et al.  Equitable and progressive distance-based user charges design and evaluation of income-based mileage fees in Maryland , 2016 .

[34]  Jun Tanimoto,et al.  A simple scaling of the effectiveness of supporting mutual cooperation in donor-recipient games by various reciprocity mechanisms , 2009, Biosyst..

[35]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

[36]  A. Pentland,et al.  Inducing Peer Pressure to Promote Cooperation , 2013, Scientific Reports.

[37]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

[38]  Jun Tanimoto,et al.  Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game , 2007, Biosyst..

[39]  Jun Tanimoto,et al.  Influence of bolstering network reciprocity in the evolutionary spatial Prisoner’s Dilemma game: a perspective , 2018, The European Physical Journal B.

[40]  Salahuddin M. Kamal,et al.  A mathematical model for the climate change: Can unpredictability offset the temptations to pollute? , 2015, Appl. Math. Comput..

[41]  Zhuxi Zhang,et al.  Heterogeneous investments promote cooperation in evolutionary public goods games , 2018, Physica A: Statistical Mechanics and its Applications.

[42]  Hyungho Youn,et al.  The effects of progressive pricing on household electricity use , 2016 .

[43]  Attila Szolnoki,et al.  Probabilistic sharing solves the problem of costly punishment , 2014, ArXiv.

[44]  Christian Hilbe,et al.  Incentives and opportunism: from the carrot to the stick , 2010, Proceedings of the Royal Society B: Biological Sciences.

[45]  M. Perc,et al.  Social diversity and promotion of cooperation in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  David G. Rand,et al.  The Evolution of Coercive Institutional Punishment , 2012, Dyn. Games Appl..

[47]  Tammo H. A. Bijmolt,et al.  Reward Redemption Effects in a Loyalty Program When Customers Choose How Much and When to Redeem , 2014 .

[48]  Attila Szolnoki,et al.  Reward and cooperation in the spatial public goods game , 2010, ArXiv.

[49]  Attila Szolnoki,et al.  Competition of tolerant strategies in the spatial public goods game , 2016, 1607.08600.

[50]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[51]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

[52]  Moustapha Diaby,et al.  Planning the supply of rewards with cooperative promotion considerations in coalition loyalty programmes management , 2015, J. Oper. Res. Soc..

[53]  Wenbo Du,et al.  Effects of taxation on the evolution of cooperation , 2018, Chaos, Solitons & Fractals.

[54]  Joseph C. Nunes,et al.  Recurring Goals and Learning: The Impact of Successful Reward Attainment on Purchase Behavior , 2011 .

[55]  Wenxing Ye,et al.  Memory-based prisoner's dilemma game with conditional selection on networks , 2017, Appl. Math. Comput..

[56]  S. Kokubo,et al.  Universal scaling for the dilemma strength in evolutionary games. , 2015, Physics of life reviews.

[57]  Thilo Gross,et al.  Shared rewarding overcomes defection traps in generalized volunteer's dilemmas. , 2013, Journal of theoretical biology.

[58]  Yi Tao,et al.  Cooperation and evolutionary dynamics in the public goods game with institutional incentives. , 2012, Journal of theoretical biology.