相关论文: Nonlinear Dynamics of the Rock-Paper-Scissors Game…
Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in ecosystem. However, the previous studies only consider the nearest- neighbor- interaction among the species. In this paper, taking the long range migration into…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate $p$ on the…
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…
A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is…
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf…
The classical game of rock-paper-scissors have inspired experiments and spatial model systems that address robustness of biological diversity. In particular the game nicely illustrates that cyclic interactions allow multiple strategies to…
The formation of out-of-equilibrium patterns is a characteristic feature of spatially-extended, biodiverse, ecological systems. Intriguing examples are provided by cyclic competition of species, as metaphorically described by the…
We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
The finitely repeated Prisoners' Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained…
The authors (Cason, Friedman and Hopkins, Reviews of Economics Studies, 2014) claimed a result that the treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. After correct two…
In this letter we consider a single parameter generalization of the standard three species Rock-Paper-Scissors (RPS) model allowing for predator-prey reversal. This model, which shall be referred to as $\kappa$RPS model, incorporates…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
Antipredator behavior is present in many biological systems where individuals collectively react to an imminent attack. The antipredator response may influence spatial pattern formation and ecosystem stability but requires an organism's…
As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated…
This work deals with a system of three distinct species that changes in time under the presence of mobility, selection, and reproduction, as in the popular rock-paper-scissors game. The novelty of the current study is the modification of…
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
We study an optimal control problem arising from a generalization of rock-paper-scissors in which the number of strategies may be selected from any positive odd number greater than 1 and in which the payoff to the winner is controlled by a…
This work investigates how biodiversity is affected in a cyclic spatial May-Leonard model with hierarchical and non-hierarchical rules. Here we propose a generalization of the traditional rock-paper-scissors model by considering highly…