934 research outputs found
Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities
The rock-paper-scissor game -- which is characterized by three strategies
R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and
R excludes S -- serves as a simple prototype for studying more complex
non-transitive systems. For well-mixed systems where interactions result in
fitness reductions of the losers exceeding fitness gains of the winners,
classical theory predicts that two strategies go extinct. The effects of
spatial heterogeneity and dispersal rates on this outcome are analyzed using a
general framework for evolutionary games in patchy landscapes. The analysis
reveals that coexistence is determined by the rates at which dominant
strategies invade a landscape occupied by the subordinate strategy (e.g. rock
invades a landscape occupied by scissors) and the rates at which subordinate
strategies get excluded in a landscape occupied by the dominant strategy (e.g.
scissor gets excluded in a landscape occupied by rock). These invasion and
exclusion rates correspond to eigenvalues of the linearized dynamics near
single strategy equilibria. Coexistence occurs when the product of the invasion
rates exceeds the product of the exclusion rates. Provided there is sufficient
spatial variation in payoffs, the analysis identifies a critical dispersal rate
required for regional persistence. For dispersal rates below , the
product of the invasion rates exceed the product of the exclusion rates and the
rock-paper-scissor metacommunities persist regionally despite being extinction
prone locally. For dispersal rates above , the product of the exclusion
rates exceed the product of the invasion rates and the strategies are
extinction prone. These results highlight the delicate interplay between
spatial heterogeneity and dispersal in mediating long-term outcomes for
evolutionary games.Comment: 31pages, 5 figure
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
We study a variant of the cyclic Lotka-Volterra model with three-agent
interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors
game, the model describes an ideal ecosystem in which cyclic competition among
three species develops through cooperative predation. Its rate equations in a
well-mixed environment display a degenerate Hopf bifurcation, occurring as
reactions involving two predators plus one prey have the same rate as reactions
involving two preys plus one predator. We estimate the magnitude of the
stochastic noise at the bifurcation point, where finite size effects turn
neutrally stable orbits into erratically diverging trajectories. In particular,
we compare analytic predictions for the extinction probability, derived in the
Fokker-Planck approximation, with numerical simulations based on the Gillespie
stochastic algorithm. We then extend the analysis of the phase portrait to
heterogeneous rates. In a well-mixed environment, we observe a continuum of
degenerate Hopf bifurcations, generalizing the above one. Neutral stability
ensues from a complex equilibrium between different reactions. Remarkably, on a
two-dimensional lattice, all bifurcations disappear as a consequence of the
spatial locality of the interactions. In the second part of the paper, we
investigate the effects of mobility in a lattice metapopulation model with
patches hosting several agents. We find that strategies propagate along the
arms of rotating spirals, as they usually do in models of cyclic dominance. We
observe propagation instabilities in the regime of large wavelengths. We also
examine three-agent interactions inducing nonlinear diffusion.Comment: 22 pages, 13 figures. v2: version accepted for publication in EPJ
Design and Construction of Zana Robot for Modeling Human Player in Rock-paper-scissors Game using Multilayer Perceptron, Radial basis Functions and Markov Algorithms
In this paper, the implementation of artificial neural networks (multilayer perceptron [MLP] and radial base functions [RBF]) and the upgraded Markov chain model have been studied and performed to identify the human behavior patterns during rock, paper, and scissors game. The main motivation of this research is the design and construction of an intelligent robot with the ability to defeat a human opponent. MATLAB software has been used to implement intelligent algorithms. After implementing the algorithms, their effectiveness in detecting human behavior pattern has been investigated. To ensure the ideal performance of the implemented model, each player played with the desired algorithms in three different stages. The results showed that the percentage of winning computer with MLP and RBF neural networks and upgraded Markov model, on average in men and women is 59%, 76.66%, and 75%, respectively. Obtained results clearly indicate a very good performance of the RBF neural network and the upgraded Markov model in the mental modeling of the human opponent in the game of rock, paper, and scissors. In the end, the designed game has been employed in both hardware and software which include the Zana intelligent robot and a digital version with a graphical user interface design on the stand. To the best knowledge of the authors, the precision of novel presented method for determining human behavior patterns was the highest precision among all of the previous studies
Cyclic game dynamics driven by iterated reasoning
Recent theories from complexity science argue that complex dynamics are
ubiquitous in social and economic systems. These claims emerge from the
analysis of individually simple agents whose collective behavior is
surprisingly complicated. However, economists have argued that iterated
reasoning--what you think I think you think--will suppress complex dynamics by
stabilizing or accelerating convergence to Nash equilibrium. We report stable
and efficient periodic behavior in human groups playing the Mod Game, a
multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for
thinking exactly one step ahead of others in their group. Groups that play this
game exhibit cycles that are inconsistent with any fixed-point solution
concept. These cycles are driven by a "hopping" behavior that is consistent
with other accounts of iterated reasoning: agents are constrained to about two
steps of iterated reasoning and learn an additional one-half step with each
session. If higher-order reasoning can be complicit in complex emergent
dynamics, then cyclic and chaotic patterns may be endogenous features of
real-world social and economic systems.Comment: 8 pages, 4 figures, and supplementary informatio
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
- …