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Public Goods Games on Coevolving Social Network Models

Tomassini, Marco, Antonioni, Alberto·2020·Frontiers in Physics
DOI 10.3389/fphy.2020.00058
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FIGURE 1 Visual representation of public goods games played on a network structure of seven nodes. Each PGG is centered in a focal node i and it is represented by a circle Gi . For example, the node a has four direct neighbors ( b , c , d , f ) and it participates in five PGGs, i.e., the circle Ga centered in a including its four neighbors, and other four PGGs represented by circles centered in its neighbors: Gb , Gc , Gd , Gf . Note that a node may indirectly interact with other nodes that are not direct neighbors. Colors represent the node contribution into the common pools in which it participates.
FIGURE 1 Visual representation of public goods games played on a network structure of seven nodes. Each PGG is centered in a focal node i and it is represented by a circle Gi . For example, the node a has four direct neighbors ( b , c , d , f ) and it participates in five PGGs, i.e., the circle Ga centered in a including its four neighbors, and other four PGGs represented by circles centered in its neighbors: Gb , Gc , Gd , Gf . Note that a node may indirectly interact with other nodes that are not direct neighbors. Colors represent the node contribution into the common pools in which it participates.CC-BY · From the PDF
FIGURE 2 Average individual contribution as a function of round number for several values of the enhancement factor r as shown in the inset. The average is taken over 40 independent repetitions of 40 rounds on a network of size 500 and α = 0.3. (A) Static case, i.e., the network topology doesn't change during the simulation. (B) Coevolving network case, i.e., unsatisfied players may redirect a link to a random group with probability p = 0.5.
FIGURE 2 Average individual contribution as a function of round number for several values of the enhancement factor r as shown in the inset. The average is taken over 40 independent repetitions of 40 rounds on a network of size 500 and α = 0.3. (A) Static case, i.e., the network topology doesn't change during the simulation. (B) Coevolving network case, i.e., unsatisfied players may redirect a link to a random group with probability p = 0.5.CC-BY · From the PDF
FIGURE 3 Average individual contribution as a function of round number for several values of the enhancement factor r as shown in the inset. The average is taken over 40 independent repetitions of 40 rounds on an initial network of size 500 and α = 0.3. (A) The probability of rewiring when an agent is unsatisfied is p = 0.2; (B) p = 0.8.
FIGURE 3 Average individual contribution as a function of round number for several values of the enhancement factor r as shown in the inset. The average is taken over 40 independent repetitions of 40 rounds on an initial network of size 500 and α = 0.3. (A) The probability of rewiring when an agent is unsatisfied is p = 0.2; (B) p = 0.8.CC-BY · From the PDF
FIGURE 4 Degree distribution functions (DDFs) and graphical representation of the corresponding network structures. Node colors represent the node contribution to the common pools in which it participates: full contribution (blue), intermediate contribution (yellow), no contribution (red). Node size corresponds to the node degree. (A) DDF of an initial network of 500 nodes built according to the procedure described in Antonioni and Tomassini [34]. (B) DDF of the evolved network after 40 rounds of play with a link redirection probability p = 0.5 and an enhancement factor r = 1.2. (C) DDF of the final evolved network after 40 rounds of play having rewiring probability p = 0.5 and enhancement factor r = 2.4. Note the different scales in DDFs and figure zooms.
FIGURE 4 Degree distribution functions (DDFs) and graphical representation of the corresponding network structures. Node colors represent the node contribution to the common pools in which it participates: full contribution (blue), intermediate contribution (yellow), no contribution (red). Node size corresponds to the node degree. (A) DDF of an initial network of 500 nodes built according to the procedure described in Antonioni and Tomassini [34]. (B) DDF of the evolved network after 40 rounds of play with a link redirection probability p = 0.5 and an enhancement factor r = 1.2. (C) DDF of the final evolved network after 40 rounds of play having rewiring probability p = 0.5 and enhancement factor r = 2.4. Note the different scales in DDFs and figure zooms.CC-BY · From the PDF
FIGURE 5 Evolution of the average clustering coefficient during a run of 40 rounds for the same r values as in Table 1 . Color codes: r = 1.2, red; r = 1.8, green; r = 2.0, yellow; r = 2.2, blue; r = 2.4, black.
FIGURE 5 Evolution of the average clustering coefficient during a run of 40 rounds for the same r values as in Table 1 . Color codes: r = 1.2, red; r = 1.8, green; r = 2.0, yellow; r = 2.2, blue; r = 2.4, black.CC-BY · From the PDF
FIGURE 6 Wikipedia 'who votes on whom' network (see text for details). Average individual contribution as a function of round number for several values of the enhancement factor r as shown in the inset. The average is taken over 40 independent repetitions of 40 rounds on the Wikipedia network using (A) p = 0 (static case); (B) p = 0.5 (coevolving).
FIGURE 6 Wikipedia 'who votes on whom' network (see text for details). Average individual contribution as a function of round number for several values of the enhancement factor r as shown in the inset. The average is taken over 40 independent repetitions of 40 rounds on the Wikipedia network using (A) p = 0 (static case); (B) p = 0.5 (coevolving).CC-BY · From the PDF

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Metadata

Authors
Tomassini, M., & Antonioni, A.
Venue
Frontiers in Physics
Publisher
Frontiers Media SA
Published
2020-03-11
Volume
8
ISSN
2296-424X
DOI
10.3389/fphy.2020.00058
Cited by
21
References
5
Licence
creativecommons.org/licenses/by/4.0/ (vor)
Funders
  • Ministerio de Economía, Industria y Competitividad, Gobierno de España
  • Ministerio de Ciencia, Innovación y Universidades

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