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Spontaneous symmetry breaking in interdependent networked game.

Jin Q, Wang L, Xia CY, Wang Z - Sci Rep (2014)

Bottom Line: Interestingly, as interdependent factor exceeds α(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks.With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity.Moreover, our results can be well predicted by the strategy-couple pair approximation method.

View Article: PubMed Central - PubMed

Affiliation: 1] Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA [2] School of Physics, Nankai University, Tianjin 300071, China.

ABSTRACT
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value α(C), the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds α(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.

No MeSH data available.


Fraction distributions of strategy couples for different value of α by using simulation (a) and SCPA approach (b). While (c) depicts the evolution patterns of stable status for different values of α. From left to right α = 0, 0.2 and 4.0, respectively. The color code of spatial patterns in (c) is the same as Fig. 4: C-C blue, C-D green, D-C yellow and D-D red (parameter: b = 1.005).
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f6: Fraction distributions of strategy couples for different value of α by using simulation (a) and SCPA approach (b). While (c) depicts the evolution patterns of stable status for different values of α. From left to right α = 0, 0.2 and 4.0, respectively. The color code of spatial patterns in (c) is the same as Fig. 4: C-C blue, C-D green, D-C yellow and D-D red (parameter: b = 1.005).

Mentions: Finally, it remains of interest to elucidate why cooperation can be improved with the increment of α. To provide answers, we study the fraction distributions of strategy couples in Fig. 6. What firstly attracts our attention is the fact that the larger the value of α is, the more C-C couples exist. Actually, as increasing α, there will be more C-D, D-C and D-D couples switching to C-C couples (in the process, D-D couples will first transform to C-D or D-C couples, then to C-C couples). In addition, Fig. 5(c) shows the spatial patterns for different α, whereby for α = 0 only a few sporadic C-C couple clusters exist, which come from the occasional superposition of cooperators' clusters on both networks, because the networks are non-relevant in such a situation. However, when a larger α is considered (α = 0.2), more C-C couples will be connected to each other in order to build solid clusters protecting themselves against the exploitation by defectors. When α equals to 0.4 (close to the symmetry breaking value αC), C-C couples strongly bond to each other, thereby much larger C-C coupled clusters will be constructed in the system, which shows us a C-C couples' ocean. At the same time, the C-D and D-C couples sporadically exist through forming small clusters and D-D couples can only survive along the edges of these small mixture strategy coupled clusters.


Spontaneous symmetry breaking in interdependent networked game.

Jin Q, Wang L, Xia CY, Wang Z - Sci Rep (2014)

Fraction distributions of strategy couples for different value of α by using simulation (a) and SCPA approach (b). While (c) depicts the evolution patterns of stable status for different values of α. From left to right α = 0, 0.2 and 4.0, respectively. The color code of spatial patterns in (c) is the same as Fig. 4: C-C blue, C-D green, D-C yellow and D-D red (parameter: b = 1.005).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3924213&req=5

f6: Fraction distributions of strategy couples for different value of α by using simulation (a) and SCPA approach (b). While (c) depicts the evolution patterns of stable status for different values of α. From left to right α = 0, 0.2 and 4.0, respectively. The color code of spatial patterns in (c) is the same as Fig. 4: C-C blue, C-D green, D-C yellow and D-D red (parameter: b = 1.005).
Mentions: Finally, it remains of interest to elucidate why cooperation can be improved with the increment of α. To provide answers, we study the fraction distributions of strategy couples in Fig. 6. What firstly attracts our attention is the fact that the larger the value of α is, the more C-C couples exist. Actually, as increasing α, there will be more C-D, D-C and D-D couples switching to C-C couples (in the process, D-D couples will first transform to C-D or D-C couples, then to C-C couples). In addition, Fig. 5(c) shows the spatial patterns for different α, whereby for α = 0 only a few sporadic C-C couple clusters exist, which come from the occasional superposition of cooperators' clusters on both networks, because the networks are non-relevant in such a situation. However, when a larger α is considered (α = 0.2), more C-C couples will be connected to each other in order to build solid clusters protecting themselves against the exploitation by defectors. When α equals to 0.4 (close to the symmetry breaking value αC), C-C couples strongly bond to each other, thereby much larger C-C coupled clusters will be constructed in the system, which shows us a C-C couples' ocean. At the same time, the C-D and D-C couples sporadically exist through forming small clusters and D-D couples can only survive along the edges of these small mixture strategy coupled clusters.

Bottom Line: Interestingly, as interdependent factor exceeds α(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks.With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity.Moreover, our results can be well predicted by the strategy-couple pair approximation method.

View Article: PubMed Central - PubMed

Affiliation: 1] Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA [2] School of Physics, Nankai University, Tianjin 300071, China.

ABSTRACT
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value α(C), the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds α(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.

No MeSH data available.