Limits...
Beyond pairwise strategy updating in the prisoner's dilemma game.

Wang X, Perc M, Liu Y, Chen X, Wang L - Sci Rep (2012)

Bottom Line: In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor.This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating.In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range.

View Article: PubMed Central - PubMed

Affiliation: Center for Complex Systems, Xidian University, Xi'an 710071, China.

ABSTRACT
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

Show MeSH

Related in: MedlinePlus

Full K – r phase diagrams, as obtained by means of Monte Carlo simulations [panels (a) and (c)] and by means of pair approximation [panels (b) and (d)].Upper red (lower blue) lines denote the boundaries between the mixed C + D and homogeneous D (C) phases.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3472391&req=5

f2: Full K – r phase diagrams, as obtained by means of Monte Carlo simulations [panels (a) and (c)] and by means of pair approximation [panels (b) and (d)].Upper red (lower blue) lines denote the boundaries between the mixed C + D and homogeneous D (C) phases.

Mentions: Further adding to the robustness of this conclusion are results presented in Fig. 2(a,c), where we present full K – r phase diagrams for both considered updating rules. It can be observed that the positive impact of local influence on the evolution of cooperation persists across large regions of K. On the other hand, the presented phase diagrams also evidence more clearly the failure of the proposed updating rule to lead to an absorbing C phase. Moreover, there is a notable qualitative difference in the critical behavior that is evoked by the updating rule. By focusing on the D → C+ D phase boundaries, it can be observed that for pairwise strategy updating there exists an optimal value of K at which cooperators thrive best. Note that the D → C + D phase boundary is bellshaped, indicating that K ≈ 0.3 is the optimal temperature at which cooperators are able to survive at the highest value of r. For strategy updating based on local influence, however, this feature is absent. The D → C + D phase boundary is in fact an inverted bell, indicating the existence of the worst rather than an optimal value of K. Notably, the results for pairwise strategy updating are in agreement with previous works626364, where it was shown that the lack of overlapping triangles, as is the case for the square lattice as well as for random regular graphs, introduces an optimal uncertainty for the evolution of cooperation. Conversely, the results obtained by considering local influence suggest that the system is behaving as if overlapping triangles were in fact present in the interaction network. Note that in the latter case an optimal K for the evolution of cooperation does not exist. This leads us to the conclusion that the interaction network is effectively altered when the local influence is taken into account. In particular, triplets of players that are not connected by means of the original interaction graph (the square lattice) become effectively connected through the joint participation of players in the same local groups (neighborhoods) that are subject to the same local influence. An identical effect was indeed observed by the study of the public goods game65, where triplets also became effectively connected because of the participation of players in the same groups. Below, we will provide further evidence concerning the effective linkage of triples of players, which is essentially a side effect of locally influenced strategy updating. Another interesting observation is that the parameter region of the mixed C + D phase in general widens as K increases, which is in contract to the results obtained by means of pairwise strategy updating.


Beyond pairwise strategy updating in the prisoner's dilemma game.

Wang X, Perc M, Liu Y, Chen X, Wang L - Sci Rep (2012)

Full K – r phase diagrams, as obtained by means of Monte Carlo simulations [panels (a) and (c)] and by means of pair approximation [panels (b) and (d)].Upper red (lower blue) lines denote the boundaries between the mixed C + D and homogeneous D (C) phases.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3472391&req=5

f2: Full K – r phase diagrams, as obtained by means of Monte Carlo simulations [panels (a) and (c)] and by means of pair approximation [panels (b) and (d)].Upper red (lower blue) lines denote the boundaries between the mixed C + D and homogeneous D (C) phases.
Mentions: Further adding to the robustness of this conclusion are results presented in Fig. 2(a,c), where we present full K – r phase diagrams for both considered updating rules. It can be observed that the positive impact of local influence on the evolution of cooperation persists across large regions of K. On the other hand, the presented phase diagrams also evidence more clearly the failure of the proposed updating rule to lead to an absorbing C phase. Moreover, there is a notable qualitative difference in the critical behavior that is evoked by the updating rule. By focusing on the D → C+ D phase boundaries, it can be observed that for pairwise strategy updating there exists an optimal value of K at which cooperators thrive best. Note that the D → C + D phase boundary is bellshaped, indicating that K ≈ 0.3 is the optimal temperature at which cooperators are able to survive at the highest value of r. For strategy updating based on local influence, however, this feature is absent. The D → C + D phase boundary is in fact an inverted bell, indicating the existence of the worst rather than an optimal value of K. Notably, the results for pairwise strategy updating are in agreement with previous works626364, where it was shown that the lack of overlapping triangles, as is the case for the square lattice as well as for random regular graphs, introduces an optimal uncertainty for the evolution of cooperation. Conversely, the results obtained by considering local influence suggest that the system is behaving as if overlapping triangles were in fact present in the interaction network. Note that in the latter case an optimal K for the evolution of cooperation does not exist. This leads us to the conclusion that the interaction network is effectively altered when the local influence is taken into account. In particular, triplets of players that are not connected by means of the original interaction graph (the square lattice) become effectively connected through the joint participation of players in the same local groups (neighborhoods) that are subject to the same local influence. An identical effect was indeed observed by the study of the public goods game65, where triplets also became effectively connected because of the participation of players in the same groups. Below, we will provide further evidence concerning the effective linkage of triples of players, which is essentially a side effect of locally influenced strategy updating. Another interesting observation is that the parameter region of the mixed C + D phase in general widens as K increases, which is in contract to the results obtained by means of pairwise strategy updating.

Bottom Line: In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor.This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating.In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range.

View Article: PubMed Central - PubMed

Affiliation: Center for Complex Systems, Xidian University, Xi'an 710071, China.

ABSTRACT
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

Show MeSH
Related in: MedlinePlus