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Game-model Research of Parrondo's Paradox Based on Network

Author: WangLinGang
Tutor: XieNengGang
School: Anhui University of
Course: Mechanical Manufacturing and Automation
Keywords: Parrondo’s paradox Coopetition behaviour BA network Adjustablenetwork of degree distribution The best probability
CLC: O157.5
Type: Master's thesis
Year: 2010
Downloads: 22
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Abstract


On the basis of Parrondo’s game, we design a biotic population game withcomplex network as its spatial carrier. Then the paper analyzes the individual’scompetitive and cooperative behaviour.The main contents include:To reflect two game relations exist in individual’s survival and evolutionaryprocess,the population’s Parrondo game model is designed:1) Zero-sum game amongindividuals(Game A) reflects the interaction relationship among individuals and theinteractions are defined as follows: competition, cooperation, Harmony-based(Harmony),Competitiveness-based(Matthew),Poor-competition-rich-cooperation(PC-RC) and random patterns;2) Negative sum-up game between individuals andenvironment(Game B). The simulation results show:1) Cooperation and competitionpatterns in any form are adaptive behavior(The average population fitness is positive).2) Contrasting the average population fitness of BA network and full connectivity, wecan identify that BA network is conducive to cooperation.3) The relationship ofindividual fitness with node degree and with clustering coefficient is disclosed. As forcooperation pattern, the greater the node degree is, the greater the individual fitnessis.With regard to nodes with the same degree, the greater the clustering coefficient is,the smaller the fitness is. For the Matthew pattern, severe polarization of individualfitness turns up, and the “Butterfly Effect” shows.4) Population’s average fitness isthe largest when the probability of playing zero-sum game is1/3in the Parrondo’sgame model.Population’s Parrondo game model is analyzed against adjustable network ofdegree distribution as spatial carrier. Moreover, network heterogeneity on adaptivecoopetition behavior is analyzed. The results show: The heterogeneity has notsignificant difference about competition,harmony and Matthew patterns, but there aretwo kinds of effects for Cooperation, PCRC and random patterns, that is positiveimpact on the fitness and negative impact on survival.Based on the capital-dependent game(Game B) of Parrondo’s Paradox for the population,we have designed history-dependent (Game B) anddimensional-dependent (Game B) Parrondo’s paradox game models for thepopulation. Then we analyzed the best probability of playing game A against thenetwork conditions and various game parameters. The simulating calculation resultsshow:1)Capital-dependent Parrondo game of the population. As for competition,Cooperation, Matthew, PCRC and random patterns, no matter what the spatial carrieris, the best probability of playing Game A is1/3; for the harmony pattern, Game Adoesn’t have the stable probability.2) Dimensional-dependent Parrondo game of thepopulation. No matter what the coopetition pattern is, for one dimensional model, thebest probability of playing Game A is0.15, while for two-dimensional model, the bestprobability of Game A is0.1.3) History-dependent Parrondo game of the population.As for competition Cooperation, Matthew and random patterns, the best probability ofplaying Game A is associated with Coopetition patterns and spatial carrier.while forharmony and PCRC patterns,there is no stable probability.Parrondo’s paradox has been used in physics so as to explain the physicalmechanism of Brownian ratchet and it is introduced into the social and biologicalsystems by the paper. The results have illustrated the rationality and adaptability ofindividual’s coopetition behavior.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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