Rock-scissors-paper game on regular small-world networks

By György Szabó, Attila Szolnoki, Rudolf Izsák. 2003

165 citations recorded by the source corpus.

The spatial rock-scissors-paper game (or cyclic Lotka–Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.

Subfields: Computer Networks and Communications, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33fc32598777d2a90a74d08a603695316cf5d80c

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In Computer Networks and Communications

In Condensed Matter Physics

In Mathematical Physics

Citations in the corpus

Evolutionary game theory: Theoretical concepts and applications to microbial communities (2010, background): “Fruitful insights into this regime have already been gained by pair approximations or larger-cluster approximations [91,119–121].”
Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game (2010, methodology): “t; S, thus strictly satisfying the prisoner’s dilemma payoﬀ ranking. As the interaction network, we use either a regular L×L square lattice, the random regular graph (RRG) constructed as described in [65], or the small-world (SW) topology with an average degree of four generated via the Watts-Stroga”
Games on graphs (2014, background): “For other graph structures, a different dynamical behavior is possible, in which the population spends increasing amounts of time dominated by each strategy in sequence [102], [103], [86], [97], [101], similar to the convergence to heteroclinic attractors found in the case of well-mixed populations ”
Stochastic population dynamics in spatially extended predator–prey systems (2017, background): “It would be interesting to investigate whether the theoretical approaches reviewed here, and devised for lattice systems, could help shed further light on the dynamics of RPS-like systems on complex random topologies, such as small-world networks on which intriguing oscillating patterns have been fo”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “[520] György Szabó, Attila Szolnoki, and Rudolf Izsák.”
Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions (2010, background): “, thereby preserving the degree distribution (i.e. every player has 4 nearest neighbors)”
Coevolutionary games - A mini review (2009, background): “Fb”