scholarly journals Dynamics, morphogenesis and convergence of evolutionary quantum Prisoner's Dilemma games on networks

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150280 ◽  
Author(s):  
Angsheng Li ◽  
Xi Yong
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Nash Equilibrium ◽  
Prisoner's Dilemma ◽  
Natural Extension ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Many Body ◽  
The Many ◽  
First Time

The authors proposed a quantum Prisoner's Dilemma (PD) game as a natural extension of the classic PD game to resolve the dilemma. Here, we establish a new Nash equilibrium principle of the game, propose the notion of convergence and discover the convergence and phase-transition phenomena of the evolutionary games on networks. We investigate the many-body extension of the game or evolutionary games in networks. For homogeneous networks, we show that entanglement guarantees a quick convergence of super cooperation, that there is a phase transition from the convergence of defection to the convergence of super cooperation, and that the threshold for the phase transitions is principally determined by the Nash equilibrium principle of the game, with an accompanying perturbation by the variations of structures of networks. For heterogeneous networks, we show that the equilibrium frequencies of super-cooperators are divergent, that entanglement guarantees emergence of super-cooperation and that there is a phase transition of the emergence with the threshold determined by the Nash equilibrium principle, accompanied by a perturbation by the variations of structures of networks. Our results explore systematically, for the first time, the dynamics, morphogenesis and convergence of evolutionary games in interacting and competing systems.

scholarly journals Evolutionary games and population dynamics: maintenance of cooperation in public goods games

2006 ◽  
Vol 273 (1600) ◽  
pp. 2565-2571 ◽  
Author(s):  
Christoph Hauert ◽  
Miranda Holmes ◽  
Michael Doebeli
Keyword(s):  
Public Goods ◽  
Prisoner's Dilemma ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Natural Extension ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Darwinian Evolution ◽  
Ecological Dynamics ◽  
Public Goods Games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

scholarly journals CORTICAL PHASE TRANSITIONS, NONEQUILIBRIUM THERMODYNAMICS AND THE TIME-DEPENDENT GINZBURG–LANDAU EQUATION

2012 ◽  
Vol 26 (06) ◽  
pp. 1250035 ◽  
Author(s):  
WALTER J. FREEMAN ◽  
ROBERTO LIVI ◽  
MASASHI OBINATA ◽  
GIUSEPPE VITIELLO
Keyword(s):  
Phase Transitions ◽  
Landau Equation ◽  
Power Laws ◽  
Time Dependent ◽  
Many Body ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Characteristic Space ◽  
The Many ◽  
The Brain

The formation of amplitude modulated and phase modulated assemblies of neurons is observed in the brain functional activity. The study of the formation of such structures requires that the analysis has to be organized in hierarchical levels, microscopic, mesoscopic, macroscopic, each with its characteristic space-time scales and the various forms of energy, electric, chemical, thermal produced and used by the brain. In this paper, we discuss the microscopic dynamics underlying the mesoscopic and the macroscopic levels and focus our attention on the thermodynamics of the nonequilibrium phase transitions. We obtain the time-dependent Ginzburg–Landau equation for the nonstationary regime and consider the formation of topologically nontrivial structures such as the vortex solution. The power laws observed in functional activities of the brain is also discussed and related to coherent states characterizing the many-body dissipative model of brain.

Lesser Antilles Lines: The Island of San Huberto (A)

2010 ◽  
pp. 1-10
Author(s):  
James V. Gelly ◽  
Phillip E. Pfeifer
Keyword(s):  
Nash Equilibrium ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Equilibrium Price ◽  
Lesser Antilles ◽  
Caribbean Island ◽  
Price Leadership ◽  
Price War

In this case, the situation is a classic duopoly. Two shipping firms are in a price war over the market for containerized shipping to and from a small Caribbean island. The case presents a table of contributions to both firms as a function of their prices. This table serves as a basis by which the class can explore the concepts of Nash equilibrium, price leadership, and prisoner’s dilemma. It is also available with the case as a student spreadsheet (QA-0355X). See also “Lesser Antilles Lines (B)” (UVA-QA-0641) and “Lesser Antilles Lines (C)” (UVA-QA-0670).

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

scholarly journals Probing the many-body localization phase transition with superconducting circuits

2019 ◽  
Vol 100 (13) ◽  
Author(s):  
Tuure Orell ◽  
Alexios A. Michailidis ◽  
Maksym Serbyn ◽  
Matti Silveri
Keyword(s):  
Phase Transition ◽  
Many Body ◽  
Superconducting Circuits ◽  
The Many

scholarly journals Punishment Effect of Prisoner Dilemma Game Based on a New Evolution Strategy Rule

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Dehui Sun ◽  
Xiaoliang Kou
Keyword(s):  
Nash Equilibrium ◽  
Prisoner's Dilemma ◽  
External Factor ◽  
Prisoner’S Dilemma ◽  
Evolution Strategy ◽  
The Stability ◽  
The Individual ◽  
Evolution Game ◽  
Stability Of Structure ◽  
Cooperation Structure

We discuss the effect of the punishment in the prisoner’s dilemma game. We propose a new evolution strategy rule which can reflect the external factor for both players in the evolution game. In general, if the punishment exists, the D (defection-defection) structure (i.e., both of the two players choose D-D strategy) which is the Nash equilibrium for the game can keep stable and never let the cooperation emerge. However, if a new evolution strategy rule is adopted, we can find that the D-D structure can not keep stable and it will decrease during the game from the simulations. In fact, the punishment mainly affects the C-D (cooperation-defection) structure in the network. After the fraction of the C-D structure achieved some levels, the punishment can keep the C-D structure stable and prevent it from transforming into C-C (cooperation-cooperation) structure. Moreover, in light of the stability of structure and the payoff of the individual gains, it can be found that the probability which is related to the payoff can affect the result of the evolution game.

scholarly journals Phase Transition of Ice at High Pressures and Low Temperatures

Molecules ◽  
2020 ◽  
Vol 25 (3) ◽  
pp. 486
Author(s):  
Jinjin Xu ◽  
Jinfeng Liu ◽  
Jinyun Liu ◽  
Wenxin Hu ◽  
Xiao He ◽  
...  
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
High Pressures ◽  
Structural Phase ◽  
Extreme Conditions ◽  
Dispersion Interactions ◽  
Many Body ◽  
Two Phases ◽  
Moller Plesset ◽  
The Many

The behavior of ice under extreme conditions undergoes the change of intermolecular binding patterns and leads to the structural phase transitions, which are needed for modeling the convection and internal structure of the giant planets and moons of the solar system as well as H2O-rich exoplanets. Such extreme conditions limit the structural explorations in laboratory but open a door for the theoretical study. The ice phases IX and XIII are located in the high pressure and low temperature region of the phase diagram. However, to the best of our knowledge, the phase transition boundary between these two phases is still not clear. In this work, based on the second-order Møller–Plesset perturbation (MP2) theory, we theoretically investigate the ice phases IX and XIII and predict their structures, vibrational spectra and Gibbs free energies at various extreme conditions, and for the first time confirm that the phase transition from ice IX to XIII can occur around 0.30 GPa and 154 K. The proposed work, taking into account the many-body electrostatic effect and the dispersion interactions from the first principles, opens up the possibility of completing the ice phase diagram and provides an efficient method to explore new phases of molecular crystals.

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