Success-driven distribution of public goods promotes cooperation but preserves defection

📝 Abstract

Established already in the Biblical times, the Matthew effect stands for the fact that in societies rich tend to get richer and the potent even more powerful. Here we investigate a game theoretical model describing the evolution of cooperation on structured populations where the distribution of public goods is driven by the reproductive success of individuals. Phase diagrams reveal that cooperation is promoted irrespective of the uncertainty by strategy adoptions and the type of interaction graph, yet the complete dominance of cooperators is elusive due to the spontaneous emergence of super-persistent defectors that owe their survival to extremely rare microscopic patterns. This indicates that success-driven mechanisms are crucial for effectively harvesting benefits from collective actions, but that they may also account for the observed persistence of maladaptive behavior.

💡 Analysis

Established already in the Biblical times, the Matthew effect stands for the fact that in societies rich tend to get richer and the potent even more powerful. Here we investigate a game theoretical model describing the evolution of cooperation on structured populations where the distribution of public goods is driven by the reproductive success of individuals. Phase diagrams reveal that cooperation is promoted irrespective of the uncertainty by strategy adoptions and the type of interaction graph, yet the complete dominance of cooperators is elusive due to the spontaneous emergence of super-persistent defectors that owe their survival to extremely rare microscopic patterns. This indicates that success-driven mechanisms are crucial for effectively harvesting benefits from collective actions, but that they may also account for the observed persistence of maladaptive behavior.

📄 Content

arXiv:1112.2558v1 [physics.soc-ph] 12 Dec 2011 Success-driven distribution of public goods promotes cooperation but preserves defection Matjaˇz Perc Faculty of Natural Sciences and Mathematics, University of Maribor, Koroˇska cesta 160, SI-2000 Maribor, Slovenia Established already in the Biblical times, the Matthew effect stands for the fact that in societies rich tend to get richer and the potent even more powerful. Here we investigate a game theoretical model describing the evolution of cooperation on structured populations where the distribution of public goods is driven by the reproductive success of individuals. Phase diagrams reveal that cooperation is promoted irrespective of the uncertainty by strategy adoptions and the type of interaction graph, yet the complete dominance of cooperators is elusive due to the spontaneous emergence of super-persistent defectors that owe their survival to extremely rare microscopic patterns. This indicates that success-driven mechanisms are crucial for effectively harvesting benefits from collective actions, but that they may also account for the observed persistence of maladaptive behavior. PACS numbers: 89.75.Fb, 87.23.Ge, 89.75.Hc The Gospel of St. Matthew states: “For to all those who have, more will be given.” Roughly two millennia latter sociologist Robert K. Merton [1] was inspired by this writ- ing and coined the term “Matthew effect” for explaining dis- crepancies in recognition received by eminent scientists and unknown researchers for similar work. A few years earlier physicist and information scientist Derek J. de Solla Price [2] actually observed the same phenomenon when studying the network of citations between scientific papers, only that he used the phrase cumulative advantage for the description. To most physicists, however, preferential attachment will be best known due to the seminal paper by Barab´asi and Albert [3], who used the concept ingeniously to explain the emergence of scaling in growing random networks. Other common varia- tions of the phrase include rich-get-richer and success-breeds- success [4], all implying that initial advantages are often self- amplifying and tend to snowball over time. No matter the wording, be it the accumulation of wealth [5] or citations [6], the making of new friends [7], or the longevity of one’s ca- reer [8], this simple yet fascinatingly powerful phenomenon arguably influences many facets of our existence. In this paper we investigate how the Matthew effect affects the evolution of cooperation in the public goods game. The public goods game [9, 10] is played in groups and captures the essential social dilemma in that collective and individual in- terests are in dissonance. Players must decide simultaneously whether they wish to contribute to the common pool or not. All the contributions are then multiplied to take into account synergetic effects of cooperation, and the resulting amount is divided equally among all group members irrespective of their initial decision. From the perspective of each individual, de- fection is clearly the rational decision to make as it yields the highest personal income if compared to other members of the group. However, if nobody decides to invest the group fails to harvest the benefits of a collective investment and the soci- ety evolves towards the “tragedy of the commons” [11]. The sustenance of cooperation in sizable groups of unrelated indi- viduals, as is the case by the public goods game, is particularly challenging since group interactions tend to blur the trails of those who defect. Unlike by pairwise interactions, reciprocity [12, 13] often fails as it is not straightforward to determine whom to reciprocate with. Social enforcement, on the other hand, may work well, although it is challenged by the fact that it is costly (see [14] for a review). Other prominent ways of promoting cooperation in public goods games include the introduction of volunteering [15], social diversity by means of complex interaction networks [16], heterogeneous wealth distributions [17], and institutionalized punishment [18]. Inspired by the seminal works on games on coevolution- ary and social networks [19–23], the most recent advances on this topic [24–28] (see [29] for a review), as well as the seem- ing omnipresence of the Matthew effect in social interactions, we consider the public goods game where the distribution of multiplied contributions is not equally shared amongst all the group members, but rather it depends on the evolutionary suc- cess of each individual. Naturally, the more successful an in- dividual is the higher its share of the public good. Assuming structured interactions, L2 players are arranged into overlapping groups of size G such that every player is surrounded by its G −1 nearest neighbors. Accordingly, each individual belongs to g = G different groups. Initially each player on site x is designated either as a cooperator (sx = C) or defector (sx = D) with equal probabil

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