scholarly journals Large deviations and Stochastic stability in Population Games

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mathias Staudigl ◽  
Srinivas Arigapudi ◽  
William H. Sandholm
Keyword(s):  
Large Deviations ◽  
Population Size ◽  
Noise Level ◽  
Large Population ◽  
Evolutionary Game ◽  
Sample Path ◽  
Game Dynamics ◽  
Population Games ◽  
Research Activities ◽  
Double Limit

<p style='text-indent:20px;'>In this article we review a model of stochastic evolution under general noisy best-response protocols, allowing the probabilities of suboptimal choices to depend on their payoff consequences. We survey the methods developed by the authors which allow for a quantitative analysis of these stochastic evolutionary game dynamics. We start with a compact survey of techniques designed to study the long run behavior in the small noise double limit (SNDL). In this regime we let the noise level in agents' decision rules to approach zero, and then the population size is formally taken to infinity. This iterated limit strategy yields a family of deterministic optimal control problems which admit an explicit analysis in many instances. We then move in by describing the main steps to analyze stochastic evolutionary game dynamics in the large population double limit (LPDL). This regime refers to the iterated limit in which first the population size is taken to infinity and then the noise level in agents' decisions vanishes. The mathematical analysis of LPDL relies on a sample-path large deviations principle for a family of Markov chains on compact polyhedra. In this setting we formulate a set of conjectures and open problems which give a clear direction for future research activities.</p>

scholarly journals A MARKOV PROCESS OF GENE FREQUENCY CHANGE IN A GEOGRAPHICALLY STRUCTURED POPULATION

Genetics ◽  
1974 ◽  
Vol 76 (2) ◽  
pp. 367-377
Author(s):  
Takeo Maruyama
Keyword(s):  
Genetic Variation ◽  
Markov Process ◽  
Diffusion Process ◽  
Gene Frequency ◽  
Transition Probabilities ◽  
Large Population ◽  
Sample Path ◽  
Time Parameter ◽  
Frequency Change ◽  
Structured Population

ABSTRACT A Markov process (chain) of gene frequency change is derived for a geographically-structured model of a population. The population consists of colonies which are connected by migration. Selection operates in each colony independently. It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population. The time parameter is a local random time that is dependent on the sample path. In fact, if the alleles are selectively neutral, the time parameter is exactly equal to the sum of the average local genetic variation appearing in the population, and otherwise they are approximately equal. The Kolmogorov forward and backward equations of the process are obtained. As a limit of large population size, a diffusion process is derived. The transition probabilities of the Markov chain and of the diffusion process are obtained explicitly. Certain quantities of biological interest are shown to be independent of the population structure. The quantities are the fixation probability of a mutant, the sum of the average local genetic variation and the variation summed over the generations in which the gene frequency in the whole population assumes a specified value.

scholarly journals Macroeconomic Impacts of Climate Change Driven by Changes in Crop Yields

2018 ◽  
Vol 10 (10) ◽  
pp. 3673 ◽  
Author(s):  
Shinichiro Fujimori ◽  
Toshichika Iizumi ◽  
Tomoko Hasegawa ◽  
Jun’ya Takakura ◽  
Kiyoshi Takahashi ◽  
...  
Keyword(s):  
Climate Change ◽  
Land Use ◽  
Population Size ◽  
Large Population ◽  
Food Prices ◽  
Production Volume ◽  
Total Uncertainty ◽  
Indicator Value ◽  
Macroeconomic Impacts ◽  
Macroeconomic Indicator

Changes in agricultural yields due to climate change will affect land use, agricultural production volume, and food prices as well as macroeconomic indicators, such as GDP, which is important as it enables one to compare climate change impacts across multiple sectors. This study considered five key uncertainty factors and estimated macroeconomic impacts due to crop yield changes using a novel integrated assessment framework. The five factors are (1) land-use change (or yield aggregation method based on spatially explicit information), (2) the amplitude of the CO2 fertilization effect, (3) the use of different climate models, (4) socioeconomic assumptions and (5) the level of mitigation stringency. We found that their global impacts on the macroeconomic indicator value were 0.02–0.06% of GDP in 2100. However, the impacts on the agricultural sector varied greatly by socioeconomic assumption. The relative contributions of these factors to the total uncertainty in the projected macroeconomic indicator value were greater in a pessimistic world scenario characterized by a large population size, low income, and low yield development than in an optimistic scenario characterized by a small population size, high income, and high yield development (0.00%).

scholarly journals Large Deviations for the Single-Server Queue and the Reneging Paradox

2021 ◽  
Author(s):  
Rami Atar ◽  
Amarjit Budhiraja ◽  
Paul Dupuis ◽  
Ruoyu Wu
Keyword(s):  
Large Deviations ◽  
Decay Rate ◽  
Sample Path ◽  
Arrival Rate ◽  
Rate Function ◽  
Service Rate ◽  
Single Server ◽  
Large Deviations Principle ◽  
Long Run ◽  
The Individual

For the M/M/1+M model at the law-of-large-numbers scale, the long-run reneging count per unit time does not depend on the individual (i.e., per customer) reneging rate. This paradoxical statement has a simple proof. Less obvious is a large deviations analogue of this fact, stated as follows: the decay rate of the probability that the long-run reneging count per unit time is atypically large or atypically small does not depend on the individual reneging rate. In this paper, the sample path large deviations principle for the model is proved and the rate function is computed. Next, large time asymptotics for the reneging rate are studied for the case when the arrival rate exceeds the service rate. The key ingredient is a calculus of variations analysis of the variational problem associated with atypical reneging. A characterization of the aforementioned decay rate, given explicitly in terms of the arrival and service rate parameters of the model, is provided yielding a precise mathematical description of this paradoxical behavior.

Lumping evolutionary game dynamics on networks

2016 ◽  
Vol 407 ◽  
pp. 328-338 ◽  
Author(s):  
G. Iacobelli ◽  
D. Madeo ◽  
C. Mocenni
Keyword(s):  
Evolutionary Game ◽  
Game Dynamics

POPULATION DYNAMICS OF SEX-DETERMINING ALLELES IN HONEY BEES AND SELF-INCOMPATIBILITY ALLELES IN PLANTS

Genetics ◽  
1979 ◽  
Vol 91 (3) ◽  
pp. 609-626 ◽  
Author(s):  
Shozo Yokoyama ◽  
Masatoshi Nei
Keyword(s):  
Population Dynamics ◽  
Population Size ◽  
Honey Bee ◽  
Honey Bees ◽  
Finite Population ◽  
Large Population ◽  
Allele Frequencies ◽  
Self Incompatibility ◽  
Overdominant Selection ◽  
Incompatibility Alleles

ABSTRACT Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is l/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from l/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.

Evaluation of several initialization methods on arithmetic optimization algorithm performance

2021 ◽  
Vol 31 (1) ◽  
pp. 70-94
Author(s):  
Jeffrey O. Agushaka ◽  
Absalom E. Ezugwu
Keyword(s):  
Population Size ◽  
Optimization Algorithm ◽  
Beta Distribution ◽  
Random Number ◽  
Large Population ◽  
Latin Hypercube Sampling ◽  
Rayleigh Distribution ◽  
Population Based ◽  
Algorithm Performance ◽  
Number Of Iterations

Abstract Arithmetic optimization algorithm (AOA) is one of the recently proposed population-based metaheuristic algorithms. The algorithmic design concept of the AOA is based on the distributive behavior of arithmetic operators, namely, multiplication (M), division (D), subtraction (S), and addition (A). Being a new metaheuristic algorithm, the need for a performance evaluation of AOA is significant to the global optimization research community and specifically to nature-inspired metaheuristic enthusiasts. This article aims to evaluate the influence of the algorithm control parameters, namely, population size and the number of iterations, on the performance of the newly proposed AOA. In addition, we also investigated and validated the influence of different initialization schemes available in the literature on the performance of the AOA. Experiments were conducted using different initialization scenarios and the first is where the population size is large and the number of iterations is low. The second scenario is when the number of iterations is high, and the population size is small. Finally, when the population size and the number of iterations are similar. The numerical results from the conducted experiments showed that AOA is sensitive to the population size and requires a large population size for optimal performance. Afterward, we initialized AOA with six initialization schemes, and their performances were tested on the classical functions and the functions defined in the CEC 2020 suite. The results were presented, and their implications were discussed. Our results showed that the performance of AOA could be influenced when the solution is initialized with schemes other than default random numbers. The Beta distribution outperformed the random number distribution in all cases for both the classical and CEC 2020 functions. The performance of uniform distribution, Rayleigh distribution, Latin hypercube sampling, and Sobol low discrepancy sequence are relatively competitive with the Random number. On the basis of our experiments’ results, we recommend that a solution size of 6,000, the number of iterations of 100, and initializing the solutions with Beta distribution will lead to AOA performing optimally for scenarios considered in our experiments.

Anadromous Sturgeons: Habitats, Threats, and Management

2007 ◽  
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Yellow River ◽  
Large Population ◽  
Leading Edge ◽  
The Yellow River ◽  
Gulf Sturgeon ◽  
Successful Recruitment ◽  
Viable Population ◽  
Size Growth

<em>Abstract.</em>—The Gulf sturgeon <em>Acipenser oxyrinchus desotoi</em> is an anadromous species listed as threatened under the Endangered Species Act in 1991. We conducted a 3year tagging study to estimate population size, growth, mortality, and age composition for sturgeon in the Yellow River. Capture probabilities and population size were estimated using Program MARK and a Cormack-Jolly–Seber model. Total mortality of Gulf sturgeon was estimated using a Beverton–Holt mortality equation. Growth rate was determined from annuli on the leading edge of pectoral fin-ray. A total of 522 Gulf sturgeon captures were made, and 399 individual fish were tagged. The population estimates for the Gulf sturgeon over 3 years ranged from 500 to 911 fish. The age structure of the population suggests successful recruitment and a viable population. The total annual mortality estimate for Yellow River Gulf sturgeon was 11.9%. Growth rate for the Yellow River population was comparable to other populations of Gulf sturgeon. The Yellow River Gulf sturgeon population is a dynamic population based upon consistent age-classes as an indicator of successful recruitment, a large population size relative to most rivers where Gulf sturgeon are found, and estimates of mortality below the reported range for the species.

Insights into the Impact of Social Networks on Evolutionary Games

2008 ◽  
pp. 306-323
Author(s):  
Katia Sycara ◽  
Paul Scerri ◽  
Anton Chechetka
Keyword(s):  
Game Theory ◽  
Social Networks ◽  
Evolutionary Game Theory ◽  
Information Diffusion ◽  
Large Population ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Agent Based ◽  
The Social ◽  
The Impact

In this chapter, we explore the use of evolutionary game theory (EGT) (Weibull, 1995; Taylor & Jonker, 1978; Nowak & May, 1993) to model the dynamics of adaptive opponent strategies for large population of players. In particular, we explore effects of information propagation through social networks in Evolutionary Games. The key underlying phenomenon that the information diffusion aims to capture is that reasoning about the experiences of acquaintances can dramatically impact the dynamics of a society. We present experimental results from agent-based simulations that show the impact of diffusion through social networks on the player strategies of an evolutionary game and the sensitivity of the dynamics to features of the social network.

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