scholarly journals Coordination and Equilibrium Selection in Games: The Role of Local Effects

2021 ◽  
Author(s):  
Tomasz Raducha ◽  
Maxi San Miguel
Keyword(s):  
Replicator Dynamics ◽  
Equilibrium Selection ◽  
System Size ◽  
Critical Value ◽  
Dominant Strategy ◽  
Coordination Games ◽  
Coordination Game ◽  
Local Effects ◽  
Update Rules

Abstract We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules – the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

scholarly journals Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dipankar Barman ◽  
Subhajit Barman ◽  
Bibhas Ranjan Majhi
Keyword(s):  
Mutual Information ◽  
Critical Point ◽  
Thermal Field ◽  
Narrow Range ◽  
Critical Value ◽  
Critical Values ◽  
Parallel Motion ◽  
Field Temperature ◽  
The Right

Abstract We investigate the effects of field temperature T(f) on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, T(f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively. While for T(f) = 0 entanglement harvesting is possible for all values of A’s acceleration aA, in the presence of temperature, it is possible only within a narrow range of aA. In (1 + 1) dimensions, the range starts from specific values and extends to infinity, and as we increase T(f), the minimum required value of aA for entanglement harvesting increases. Moreover, above a critical value aA = ac harvesting increases as we increase T(f), which is just opposite to the accelerations below it. There are several critical values in (1 + 3) dimensions when they are in different accelerations. Contrary to the single range in (1 + 1) dimensions, here harvesting is possible within several discrete ranges of aA. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to (1 + 1) dimensional results. We also discuss the dependence of mutual information among these detectors on aA and T(f).

scholarly journals Regulation of the normalized rate of driven magnetic reconnection through shocked flux pileup

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Joseph Olson ◽  
Jan Egedal ◽  
Michael Clark ◽  
Douglass A. Endrizzi ◽  
Samuel Greess ◽  
...  
Keyword(s):  
Magnetic Reconnection ◽  
System Size ◽  
Force Balance ◽  
Absolute Rate ◽  
Reconnection Rate ◽  
Supersonic Plasma ◽  
Reconnection Layer ◽  
Inflow Conditions ◽  
Theoretical Results

Magnetic reconnection is explored on the Terrestrial Reconnection Experiment (TREX) for asymmetric inflow conditions and in a configuration where the absolute rate of reconnection is set by an external drive. Magnetic pileup enhances the upstream magnetic field of the high-density inflow, leading to an increased upstream Alfvén speed and helping to lower the normalized reconnection rate to values expected from theoretical consideration. In addition, a shock interface between the far upstream supersonic plasma inflow and the region of magnetic flux pileup is observed, important to the overall force balance of the system, thereby demonstrating the role of shock formation for configurations including a supersonically driven inflow. Despite the specialized geometry where a strong reconnection drive is applied from only one side of the reconnection layer, previous numerical and theoretical results remain robust and are shown to accurately predict the normalized rate of reconnection for the range of system sizes considered. This experimental rate of reconnection is dependent on system size, reaching values as high as 0.8 at the smallest normalized system size applied.

THE TALENT VERSUS LUCK MODEL AS AN ENSEMBLE OF ONE-DIMENSIONAL RANDOM WALKS

2021 ◽  
Author(s):  
RICARDO SIMÃO ◽  
FRANCISCO ROSENDO ◽  
LUCAS WARDIL
Keyword(s):  
Random Walks ◽  
Critical Value ◽  
One Dimensional ◽  
Sequence Of Events ◽  
Long Run ◽  
Large Fluctuations ◽  
Two Factors ◽  
Individual Success ◽  
Shed Light

The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.

scholarly journals The Role of Dispersal in Interacting Patches Subject to an Allee Effect

2013 ◽  
Vol 45 (4) ◽  
pp. 1182-1197
Author(s):  
N. Lanchier
Keyword(s):  
Allee Effect ◽  
Interacting Particle Systems ◽  
Local Population ◽  
Critical Value ◽  
Initial Distribution ◽  
Interacting Particle ◽  
Strong Allee Effect ◽  
Long Term Behavior

This article is concerned with a stochastic multipatch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that was recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to ∞, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large, whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, fast long-range dispersal drives the population toward extinction.

Effects of TiO2 on the Viscocity and Solidification Temperature of Mold Fluxes for the Stainless Steel

2011 ◽  
Vol 189-193 ◽  
pp. 107-113 ◽  
Author(s):  
Li Feng Sun ◽  
Hong Po Wang ◽  
Mao Fa Jiang ◽  
Qi Zeng Lin ◽  
Chun Lai Liu ◽  
...  
Keyword(s):  
Stainless Steel ◽  
Critical Value ◽  
Solidification Temperature ◽  
Network Modifier ◽  
Mold Fluxes ◽  
Rotary Viscometer

Effects of TiO2 on the viscous characteristic of mold fluxes for the stainless steel were investigated by the rotary viscometer, TEM and XRD. The results showed that with the increasing amount of additive TiO2, the viscosity and solidification temperature of mold fluxes could decrease gradually, and then increase rapidly. The viscosity and solidification temperature of mold fluxes were minimum of 0.30Pa.s (1300°С ) and 1198°С respectively, as amount of additive TiO2 was 10mass%. The viscosity of mold fluxes could be decreased by the additive TiO2 which played the role of network modifier, and could be increased by the precipitation of perovskite (CaTiO3) crystals as amount of additive TiO2 was more than the critical value. The growth of cuspidine and wollastonite crystals could be restrained, and the precipitation of perovskite and melilite crystals could be promoted by the additive TiO2. In this study, the solubility of additive TiO2 was more than 20mass% in mold fluxes at 1350°С .

One-point turbulence structure tensors

2001 ◽  
Vol 428 ◽  
pp. 213-248 ◽  
Author(s):  
S. C. KASSINOS ◽  
W. C. REYNOLDS ◽  
M. M. ROGERS
Keyword(s):  
Turbulence Structure ◽  
Turbulence Statistics ◽  
Local Effects ◽  
Statistical Measures ◽  
Non Local ◽  
The One ◽  
Rate Correlation ◽  
Systematic Framework ◽  
Structure Tensors

The dynamics of the evolution of turbulence statistics depend on the structure of the turbulence. For example, wavenumber anisotropy in homogeneous turbulence is known to affect both the interaction between large and small scales (Kida & Hunt 1989), and the non-local effects of the pressure–strain-rate correlation in the one-point Reynolds stress equations (Reynolds 1989; Cambon et al. 1992). Good quantitative measures of turbulence structure are easy to construct using two-point or spectral data, but one-point measures are needed for the Reynolds-averaged modelling of engineering flows. Here we introduce a systematic framework for exploring the role of turbulence structure in the evolution of one-point turbulence statistics. Five one-point statistical measures of the energy-containing turbulence structure are introduced and used with direct numerical simulations to analyse the role of turbulence structure in several cases of homogeneous and inhomogeneous turbulence undergoing diverse modes of mean deformation. The one-point structure tensors are found to be useful descriptors of turbulence structure, and lead to a deeper understanding of some rather surprising observations from DNS and experiments.

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