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Register a new userA Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game
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Wenyi Zhang
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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In this paper, a nonlinear revision protocol is proposed and embedded into the traffic evolution equation of the classical proportional-switch adjustment process (PAP), developing the present nonlinear pairwise swapping dynamics (NPSD) to describe the selfish rerouting evolutionary game. It is demonstrated that i) NPSD and PAP require the same amount of network information acquisition in the route-swaps, ii) NPSD is able to prevent the over-swapping deficiency under a plausible behavior description; iii) NPSD can maintain the solution invariance, which makes the trial and error process to identify a feasible step-length in a NPSD-based swapping algorithm is unnecessary, and iv) NPSD is a rational behavior swapping process and the continuous-time NPSD is globally convergent. Using the day-to-day NPSD, a numerical example is conducted to explore the effects of the reaction sensitivity on traffic evolution and characterize the convergence of discrete-time NPSD.
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Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.
This paper is dealing with another multiple person game model under the antagonistic duel type setup. The most flexible multiple person duel game is analytically solved and the explicit formulas are solved to determine the time dependent duel game model by using the first exceed theory. Unlike conventional two-person duel game, multiple battle fields are introduced in the paper and each battle field becomes shooting ground of pairwise players. This model is targeted for real-world situations especially for selected target shooting scenarios. An analogue of the theory in the paper is designed for solving the best shooting time within multiple battle fields. This new proposed model is fully mathematically explained to be adapted in various domains including the strategies and operations.
We propose an extended spatial evolutionary public goods game (SEPGG) model to study the dynamics of individual career choice and the corresponding social output. Based on the social value orientation theory, we categorized two classes of work, namely the public work if it serves public interests, and the private work if it serves personal interests. Under the context of SEPGG, choosing public work is to cooperate and choosing private work is to defect. We then investigate the effects of employee productivity, human capital and external subsidies on individual career choices of the two work types, as well as the overall social welfare. From simulation results, we found that when employee productivity of public work is low, people are more willing to enter the private sector. Although this will make both the effort level and human capital of individuals doing private work higher than those engaging in public work, the total outcome of the private sector is still lower than that of the public sector provided a low level of public subsidies. When the employee productivity is higher for public work, a certain amount of subsidy can greatly improve system output. On the contrary, when the employee productivity of public work is low, provisions of subsidy to the public sector can result in a decline in social output.
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evolutionary game theory and review basic properties of deterministic replicator dynamics and stochastic dynamics of finite populations. We discuss stability of equilibria in deterministic dynamics with migration, time-delay, and in stochastic dynamics of well-mixed populations and spatial games with local interactions. We analyze the dependence of the long-run behaviour of a population on various parameters such as the time delay, the noise level, and the size of the population.
Since the sequencing of large genomes, many statistical features of their sequences have been found. One intriguing feature is that certain subsequences are much more abundant than others. In fact, abundances of subsequences of a given length are distributed with a scale-free power-law tail, resembling properties of human texts, such as the Zipfs law. Despite recent efforts, the understanding of this phenomenon is still lacking. Here we find that selfish DNA elements, such as those belonging to the Alu family of repeats, dominate the power-law tail. Interestingly, for the Alu elements the power-law exponent increases with the length of the considered subsequences. Motivated by these observations, we develop a model of selfish DNA expansion. The predictions of this model qualitatively and quantitatively agree with the empirical observations. This allows us to estimate parameters for the process of selfish DNA spreading in a genome during its evolution. The obtained results shed light on how evolution of selfish DNA elements shapes non-trivial statistical properties of genomes.
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