scholarly journals Rock-Paper-Scissors Lattice Model

2020 ◽  
Vol 16 (4) ◽  
pp. 400-402
Author(s):  
Nasir Ganikhodjaev ◽  
Pah Chin Hee
Keyword(s):  
Lattice Model ◽  
Statistical Physics ◽  
Lattice Models ◽  
Evolutionary Games ◽  
Payoff Matrix ◽  
Ergodic Transformation ◽  
Translation Invariant ◽  
Periodic Gibbs Measure ◽  
Quadratic Stochastic Operators ◽  
Player Game

In this work, we introduce Rock-Paper-Scissors lattice model on Cayley tree of second order generated by Rock-Paper-Scissors game. In this strategic 2-player game, the rule is simple: rock beats scissors, scissors beat paper, and paper beats rock. A payoff matrix  of this game is a skew-symmetric. It is known that quadratic stochastic operator generated by this matrix is non-ergodic transformation. The Hamiltonian of Rock-Paper-Scissors Lattice Model is defined by this skew-symmetric payoff matrix . In this paper, we discuss a connection between three fields of research: evolutionary games, quadratic stochastic operators, and lattice models of statistical physics. We prove that a phase diagram of the Rock-Paper-Scissors model consists of translation-invariant and periodic Gibbs measure with period 3.

scholarly journals Convergent perturbation theory for lattice models with fermions

2016 ◽  
Vol 31 (13) ◽  
pp. 1650072 ◽  
Author(s):  
V. K. Sazonov
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Expansions ◽  
Lattice Model ◽  
Lattice Models ◽  
Convergent Series ◽  
Standard Perturbation Theory

The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.

GENERALIZED SKLYANIN ALGEBRA AND INTEGRABLE LATTICE MODELS

1994 ◽  
Vol 09 (13) ◽  
pp. 2245-2281 ◽  
Author(s):  
YAS-HIRO QUANO
Keyword(s):  
Inverse Problem ◽  
Lattice Model ◽  
Lattice Models ◽  
Baxter Equation ◽  
Initial Condition ◽  
Infinite Dimensional ◽  
Integrable Lattice ◽  
Crossing Symmetry ◽  
Sklyanin Algebra ◽  
Integrable Lattice Models

We study three properties of the ℤn⊗ℤn-symmetric lattice model; i.e. the initial condition, the unitarity and the crossing symmetry. The scalar factors appearing in the unitarity and the crossing symmetry are explicitly obtained. The [Formula: see text]-Sklyanin algebra is introduced in the natural framework of the inverse problem for this model. We build both finite- and infinite-dimensional representations of the [Formula: see text]-Sklyanin algebra, and construct an [Formula: see text] generalization of the broken ℤN model. Furthermore, the Yang-Baxter equation for this new model is proved.

scholarly journals Slow dynamics in translation-invariant quantum lattice models

2018 ◽  
Vol 97 (10) ◽  
Author(s):  
Alexios A. Michailidis ◽  
Marko Žnidarič ◽  
Mariya Medvedyeva ◽  
Dmitry A. Abanin ◽  
Tomaž Prosen ◽  
...  
Keyword(s):  
Lattice Models ◽  
Slow Dynamics ◽  
Quantum Lattice ◽  
Translation Invariant ◽  
Invariant Quantum

scholarly journals Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree

2015 ◽  
Vol 18 (01) ◽  
pp. 1550006 ◽  
Author(s):  
U. A. Rozikov ◽  
F. H. Haydarov
Keyword(s):  
Gibbs Measure ◽  
Cayley Tree ◽  
Nearest Neighbor ◽  
Gibbs Measures ◽  
Sufficient Condition ◽  
Translation Invariant ◽  
Periodic Gibbs Measure

We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 1. We show that periodic Gibbs measures are either translation-invariant or periodic with period two. We describe two-periodic Gibbs measures of the model. For k = 1 we show that there is no any periodic Gibbs measure. In case k ≥ 2 we get a sufficient condition on Hamiltonian of the model with uncountable set of spin values under which the model has no periodic Gibbs measure. We construct several models which have at least two periodic Gibbs measures.

scholarly journals Multi-Player Evolutionary Game of Network Attack and Defense Based on System Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3014
Author(s):  
Pengxi Yang ◽  
Fei Gao ◽  
Hua Zhang
Keyword(s):  
Evolutionary Game ◽  
Stable State ◽  
Payoff Matrix ◽  
Game Model ◽  
Network Attack ◽  
Evolutionary Stable Strategies ◽  
Player Game ◽  
Attack And Defense ◽  
Mathematical Derivation

We formalize the adversarial process between defender and attackers as a game and study the non-cooperative evolutionary game mechanism under bounded rationality. We analyze the long-term dynamic process between the attacking and defending parties using the evolutionary stable strategies derived from the evolutionary game model. First, we construct a multi-player evolutionary game model consisting of a defender and multiple attackers, formally describe the strategies, and construct a three-player game payoff matrix. Then, we propose two punishment schemes, i.e., static and dynamic ones. Moreover, through the combination of mathematical derivation with simulation, we obtain the evolutionary stable strategies of each player. Different from previous work, in this paper, we consider the influence of strategies among different attackers. The simulation shows that (1) in the static punishment scheme, increasing the penalty can quickly control the occurrence of network attacks in the short term; (2) in the dynamic punishment scheme, the game can be stabilized effectively, and the stable state and equilibrium values are not affected by the change of the initial values.

scholarly journals A Two-Player Iterated Survival Game

2018 ◽  
Author(s):  
John Wakeley ◽  
Martin Nowak
Keyword(s):  
Overall Survival ◽  
High Probability ◽  
Evolutionary Games ◽  
Single Step ◽  
Mixed Population ◽  
Pairwise Interactions ◽  
Player Game ◽  
Expected Payoffs ◽  
Number Of Iterations ◽  
Over Time

AbstractWe describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies. We consider individuals with hardwired, unconditional behaviors or strategies. When both players are present, each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as n increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well-mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent’s type without modification and fitnesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit (n → ∞). Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other pair and for either type when it is alone, then cooperation becomes favored if the number of iterations is large enough. This holds regardless of the structure of pairwise interactions in a single step. Even if the single-step interaction is a Prisoner’s Dilemma, the cooperative type becomes favored. Enhanced survival is crucial in these iterated evolutionary games: if players in pairs start the game with a fitness deficit relative to lone individuals, the prospects for cooperation can become even worse than in the case of a single-step game.

scholarly journals A resource-based game theoretical approach for the paradox of the plankton

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2329 ◽  
Author(s):  
Weini Huang ◽  
Paulo Roberto de Araujo Campos ◽  
Viviane Moraes de Oliveira ◽  
Fernando Fagundes Ferrreira
Keyword(s):  
Species Diversity ◽  
Competitive Exclusion ◽  
Evolutionary Games ◽  
Payoff Matrix ◽  
Central Focus ◽  
Number Of Species ◽  
High Species Diversity ◽  
Game Theoretical Approach ◽  
Plankton Communities ◽  
Over Time

The maintenance of species diversity is a central focus in ecology. It is not rare to observe more species than the number of limiting resources, especially in plankton communities. However, such high species diversity is hard to achieve in theory under the competitive exclusion principles, known as the plankton paradox. Previous studies often focus on the coexistence of predefined species and ignore the fact that species can evolve. We model multi-resource competitions using evolutionary games, where the number of species fluctuates under extinction and the appearance of new species. The interspecific and intraspecific competitions are captured by a dynamical payoff matrix, which has a size of the number of species. The competition strength (payoff entries) is obtained from comparing the capability of species in consuming resources, which can change over time. This allows for the robust coexistence of a large number of species, providing a possible solution to the plankton paradox.

COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE MODEL BASED ON THE NEHRING–SAUPE INTERACTION POTENTIAL

1999 ◽  
Vol 13 (32) ◽  
pp. 3879-3902 ◽  
Author(s):  
R. HASHIM ◽  
S. ROMANO
Keyword(s):  
Lattice Model ◽  
Lattice Models ◽  
Interaction Potentials ◽  
Cylindrically Symmetric ◽  
Positive Quantity ◽  
Nearest Neighbours ◽  
Anisotropic Lattice ◽  
Scalar Products ◽  
Scalar Invariants ◽  
Unit Vectors

By now, nematogenic lattice models have been extensively studied in the literature; they usually involve cylindrically symmetric (uniaxial) particles and isotropic interaction potentials defined by even functions of the scalar products between unit vectors defining their orientations; anisotropic interaction potentials involving other scalar invariants, i.e. also depending on the orientations of the two particles with respect to the intermolecular vector, have been considered far less often. A model of the latter kind was proposed by Nehring and Saupe over 25 years ago; we have considered here its restriction to nearest neighbours, having the form [Formula: see text] Here the three-component vectors xj∈ Z3define centre-of-mass coordinates of the particles, and ukare three-component unit vectors defining their orientations; ∊ is a positive quantity setting energy and temperature scales (i.e. T*=kBT/∊); this model is seen to be the anisotropic counterpart to the generic Lebwohl–Lasher lattice model.The model has been addressed by simulation; comparisons are reported with other anisotropic lattice models recently studied in the literature.

Elastic Constants and Pair Potentials for Nematogenic Lattice Models

1998 ◽  
Vol 12 (22) ◽  
pp. 2305-2323 ◽  
Author(s):  
S. Romano
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Free Energy ◽  
Energy Density ◽  
Boundary Conditions ◽  
Elastic Constants ◽  
Lattice Model ◽  
Pair Potential ◽  
Lattice Models ◽  
Free Energy Density

Director configurations in nematic Liquid Crystals can be determined by minimizing their elastic free-energy density, on the basis of elastic constants and of specific boundary conditions; in some published cases, this has been obtained by numerical procedures where the elastic free-energy density plays the same role as the overall potential energy in a standard Monte Carlo simulation. The "potentials" used in these papers are short-ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to the well-known Lebwohl–Lasher lattice model.On the other hand, one can construct, possibly in different ways, a lattice model with pairwise additive interactions, approximately reproducing the elastic free-energy density, where parameters defining the pair potential are expressed as linear combinations of elastic constants; a nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (T. Gruhn and S. Hess, Z. Naturforsch.A51, 1 (1996)), has been investigated here by Monte Carlo simulation with periodic boundary conditions, i.e. aimed at the resulting bulk behavior.

Sign in / Sign up

Export Citation Format

Share Document