Reputation-based partner choice promotes cooperation in social networks

Feng Fu, Christoph Hauert, Martin A. Nowak, and Long Wang

Phys. Rev. E 78, 026117 – Published 22 August 2008

Abstract

We investigate the cooperation dynamics attributed to the interplay between the evolution of individual strategies and evolution of individual partnerships. We focus on the effect of reputation on an individual’s partner-switching process. We assume that individuals can either change their strategies by imitating their partners or adjust their partnerships based on local information about reputations. We manipulate the partner switching in two ways; that is, individuals can switch from the lowest reputation partners, either to their partners’ partners who have the highest reputation (i.e., ordering in partnership) or to others randomly chosen from the entire population (i.e., randomness in partnership). We show that when individuals are able to alter their behavioral strategies and their social interaction partnerships on the basis of reputation, cooperation can prevail. We find that the larger temptation to defect and the denser the partner network, the more frequently individuals need to shift their partnerships in order for cooperation to thrive. Furthermore, an increasing tendency of switching to partners’ partners is more likely to lead to a higher level of cooperation. We show that when reputation is absent in such partner-switching processes, cooperation is much less favored than that of the reputation involved. Moreover, we investigate the effect of discounting an individual’s reputation on the evolution of cooperation. Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships.

Received 15 May 2008

DOI:https://doi.org/10.1103/PhysRevE.78.026117

Authors & Affiliations

Feng Fu^1,2, Christoph Hauert^1,3, Martin A. Nowak^1,4,*, and Long Wang^2,†

¹Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
²Center for Systems and Control, College of Engineering and Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing 100871, China
³Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada V6T 1Z2
⁴Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA

^*martiṉnowak@harvard.edu
^†longwang@pku.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 78, Iss. 2 — August 2008

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Dynamics of strategies and partner networks: (a) fraction of cooperators, (b) fraction of $C C ∕ C D ∕ D D$ links, (c) cumulative degree distribution of the resulting partner network at final state, and (d) degree-dependent reputation score $R (k)$ , which is averaged over nodes with degree $k$ at final state. Cooperation evolves under reputation-based partner switching. The emergent partner network in this case is disassortative (assortativity coefficient $r = - 0.3937$ ) and highly heterogeneous. The amount of heterogeneity of the partner network increases as individuals adjust their partners selectively according to reputation. Individuals with good reputations tend to attract new partnerships, while those with low reputations are confronted with the threat of losing existing partnerships. Thus under this social selection pressure, individuals are forced to be generous in order to obtain a good reputation. This positive feedback can drive the system up to full cooperation. Parameter values are $N = 10^{4}$ , $⟨ k ⟩ = 10$ , $b = 1.2$ , $W = 1$ , $p = 0.5$ , and $β = 0.01$ . Initially, cooperators and defectors are uniformly distributed in the partner network with equal probability.Reuse & Permissions
Figure 2
The effects of the temptation to defect [panel (a)] and the average degree [panel (b)] on the evolution of cooperation. The fraction of cooperation is plotted as a function of the time scale ratio, $w$ , between strategy updating and partner switching. Cooperation becomes dominant when individuals sufficiently often adjust their partnerships based on reputation. Furthermore, the larger the temptation to defect and the more number of interaction partners on average, the more promptly individuals need to change their partnerships in order for cooperation to thrive. Parameter values are (a) $N = 10^{3}$ , $⟨ k ⟩ = 10$ , $p = 0.5$ , and $β = 0.01$ and (b) $N = 10^{3}$ , $b = 1.5$ , $p = 0.5$ , and $β = 0.01$ . In this figure and subsequent ones, each data point results from averaging over $10^{3}$ independent runs.Reuse & Permissions
Figure 3
The influence of “ordering” in partner switching on the evolution of cooperation. When individuals tend to switch to partners’ partners with good reputation, cooperation is favored. Parameter values are $N = 10^{3}$ , $⟨ k ⟩ = 10$ , $β = 0.01$ , $W = 0.1$ , and $b = 1.2$ .Reuse & Permissions
Figure 4
(Color online). The effect of reputation on the evolution of cooperation. When there is no reputation involved in partner switching, the cooperation level is much lower. Compared with the original model without discounting of reputation $(δ = 1)$ , decaying memory in reputation (here, $δ = 0.5$ ) leads to a lower cooperation level when individuals occasionally shift their partners; in contrast, discounting of reputation provides a more advantageous environment for cooperation when individuals frequently change their partners. Parameter values are $N = 10^{3}$ , $⟨ k ⟩ = 10$ , $β = 0.01$ , $b = 1.4$ , and $p = 0.5$ .Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics