A game theory model of urban public traffic networks

We have studied urban public traffic networks from the viewpoint of complex networks and game theory. Firstly, we have empirically investigated an urban public traffic network in Beijing in 2003, and obtained its statistical properties. Then a simplified game theory model is proposed for simulating the evolution of the traffic network. The basic idea is that three network manipulators, passengers, an urban public traffic company, and a government traffic management agency, play games in a network evolution process. Each manipulator tries to build the traffic lines to magnify its “benefit”. Simulation results show a good qualitative agreement with the empirical results.     

Evolutionary game theory: Theoretical concepts and applications to microbial communities

Ecological systems are complex assemblies of large numbers of individuals, interacting competitively under multifaceted environmental conditions. Recent studies using microbial laboratory communities have revealed some of the self-organization principles underneath the complexity of these systems. A major role of the inherent stochasticity of its dynamics and the spatial segregation of different interacting species into distinct patterns has thereby been established. It ensures the viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of “social” behavior.A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the mathematical tools and a conceptual framework for a deeper understanding of these ecological systems. We give an introduction into the modern formulation of these theories and illustrate their effectiveness focussing on selected examples of microbial systems. Intrinsic fluctuations, stemming from the discreteness of individuals, are ubiquitous, and can have an important impact on the stability of ecosystems. In the absence of speciation, extinction of species is unavoidable. It may, however, take very long times. We provide a general concept for defining survival and extinction on ecological time-scales. Spatial degrees of freedom come with a certain mobility of individuals. When the latter is sufficiently high, bacterial community structures can be understood through mapping individual-based models, in a continuum approach, onto stochastic partial differential equations. These allow progress using methods of nonlinear dynamics such as bifurcation analysis and invariant manifolds. We conclude with a perspective on the current challenges in quantifying bacterial pattern formation, and how this might have an impact on fundamental research in non-equilibrium physics.     

An evolutionary game theory model of binary opinion formation

A basic characteristic of most opinion models is that people tend to agree or compromise in the opinion interaction, which could be hopefully described by cooperative games in the evolutionary game theory framework. This paper presents game theory methods to model the formation of binary opinions: cooperative games are proposed to model the interaction rules of general people who tend to find an agreement; minority games are proposed to model the behaviors of contrarians; opinion preference is considered by varying the payoff values. The Majority Voter model could be restored from the proposed games. The game theory models show evolutionary results similar to traditional opinion models. Specially, the evolution of opinions with consideration of contrarians is in accordance with the Galam model. Furthermore, influences of evolving rule, network topology and initial distribution of opinions are studied through numerical simulations. Discussions about methods to promote or hinder the consensus state at the best equilibrium point are given.     

Kinetics of a first-order phase transition: computer simulations and theory

We make a quantitative comparison between the predictions of the Becker-Döring equations and computer simulations on a model of a quenched binary A-B alloy. The atoms are confined to the vertices of a simple cubic lattice, interact through attractive nearest neighbor interactions, and move by interchanges of nearest neighbor pairs (Kawasaki dynamics). We study in particular the time evolution of the number of clusters of A atoms of each size, at four different concentrations: _A=0.035, 0.05, 0.075, and 0.1 atoms per lattice site. The temperature is 0.59 times the critical temperature. At this temperature the equilibrium concentration of A atoms in the B-rich phase is _A ^eq =0.0145 atoms/lattice site. The coefficients entering the Becker-Döring equations are obtained by extrapolation from previously published low-density calculations, leaving the time scale as the only adjustable parameter. We find good agreement at the three lower densities. At 10% density the agreement is, as might be expected, less satisfactory but still fairly good-indicating a quite wide range of utility for the Becker-Döring equations.Supported in part by NSF Grant DMR81-14726 and DOE Contract DE-AC02-76ERO3077.     

Existence theory of the linear equations appearing in the Chapman-Enskog solutions to two kinetic equations for liquids

The linear operators appearing in the Chapman-Enskog solutions to Kirkwood's Fokker-Planck kinetic equation and to Rice and Allnatt's kinetic equation are studied in this article. Existence proofs are given for the linearized Chapman-Enskog equations involving either the Fokker-Planck or the Rice-Allnatt operators. It is shown that the Fokker-Planck and Rice-Allnatt operators, defined in the domain appropriate to kinetic theory, are essentially self-adjoint. It is also shown that the spectrum of either of these operators coincides with the spectrum of the self-adjoint extension of the corresponding operator.Sloan Foundation Fellow 1968–70. Guggenheim Fellow 1969–70.     

A spectrum handoff scheme for optimal network selection in Cognitive Radio vehicular networks: A game theoretic auction theory approach

The recent strides in vehicular networks have emerged as a convergence of multi radio access networks having different user preferences, multiple application requirements and multiple device types. In future Cognitive Radio (CR) vehicular networks deployment, multiple radio access networks may coexist in the overlapping areas having different characteristics in terms of multiple attributes. Hence, it becomes a challenge for CR vehicular node to select the optimal network for the spectrum handoff decision. A game theoretic auction theory approach is interdisciplinary effective approach to select the optimal network for spectrum handoff. The competition between different CR vehicular node and access networks can be formulated as multi-bidder bidding to provide its services to CR vehicular node. The game theory is the branch of applied mathematics which make intelligent decision to select the optimal alternative from predetermined alternatives. Hence, this paper investigates a spectrum handoff scheme for optimal network selection using game theoretic auction theory approach in CR vehicular networks. The paper has also proposed a new cost function based multiple attribute decision making method which outperforms other existing methods. Numerical results revel that the proposed scheme is effective for spectrum handoff for optimal network selection among multiple available networks.     

Partition density functional theory and its extension to the spin-polarized case

Partition density functional theory (PDFT) [P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82 (2), 024501 (2010)] is a formally exact method for obtaining molecular properties from Kohn–Sham calculations on isolated fragments. Here, we express the partition energy of PDFT as an implicit functional of the molecular spin-densities for a given choice of fragmentation, and use the principle of von Barth and Hedin to formulate the spin-decomposed version of PDFT. We introduce a partition energy functional of the spin-up and spin-down electronic densities and derive the associated polarized partition potentials, which are found to be global quantities that influence every fragment in the molecule. Along with the formal theory, we propose a simplified approach to computing the spin-partition potentials, and illustrate its utility and accuracy with two simple examples. Finally, we propose a viable approach to including external electric and magnetic fields in the framework of spin-PDFT.     

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.     

Doves and hawks in economics revisited: An evolutionary quantum game theory based analysis of financial crises

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as a consequence of the financial crisis, it would be desirable to change the “rules of the game” in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the well-known hawk-dove game by a quantum approach, we can show that dependent on entanglement, evolutionary stable strategies also can emerge, which are not predicted by the classical evolutionary game theory and where the total economic population uses a non-aggressive quantum strategy.     

表象变换和久期微扰理论在耦合杜芬方程中的应用

本文通过对耦合杜芬方程线性项的表象变换及非线性项的久期微扰理论的应用,将耦合杜芬方程转化为简正表象下的退耦合形式,由此可以很方便地得出耦合杜芬方程的解.为了验证该方法的正确性,设计了音叉耦合实验,观测到了振幅谱谱峰的劈裂以及"振滞回线"现象,这些实验结果都可以和之前所得的理论结果符合得很好.本文求解耦合非线性方程的方法...     

用含时微扰理论计算Landau体系的光致跃迁概率

用含时微扰理论计算了Landau体系的光致跃迁概率,得到其偶极跃迁中的末态只是初态的最邻近态的结果．     

On the invariance of constitutive equations according to the kinetic theory of gases

Iterative techniques for solving the Boltzmann equation in the kinetic theory of gases yield expressions for the stress tensor and heat flux vector that are analogous to constitutive equations in continuum mechanics. However, these expressions are not generally invariant under the Euclidean group of transformations, whereas constitutive equations in continuum mechanics are usually required to be by the principle of material frame indifference. This disparity in invariance properties has led some previous investigators to argue that Euclidean invariance should be discarded as a contraint on constitutive equations. It is proven mathematically in this paper that the results of the Chapman-Enskog iterative procedure have no direct bearing on this issue. In order to settle this question, it is necessary to examine mathematically the effect of superimposed rigid body rotations on solutions of the Boltzmann equation. A preliminary investigation along these lines is presented which suggests that the kinetic theory is consistent with material frame indifference in at least a strong approximate sense provided that the disparity in the time scales of the microscopic and macroscopic motions is extremely large—a condition which is usually a prerequisite for the existence of constitutive equations.On leave from Stevens Institute of Technology, Hoboken, New Jersey 07030.     

A statistical-mechanical theory of slow dynamics near the glass transition

A statistical-mechanical theory of slow dynamics near the glass transition in two kinds of glass-forming systems, (M) molecular systems and (S) suspensions of colloids, is presented from a unified point of view based on the Tokuyama-Mori projection operator method. The exact diffusion equations for the coherent- and the incoherent-intermediate scattering functions are first derived, whose memory functions are convolutionless in time and contain the correlation effects due to the hydrodynamic interactions in (S). The analytic expressions of the memory functions are then calculated within the mode-coupling theory (MCT) approximation and are shown to coincide with the conventional ones obtained by MCT. Alternative mode-coupling equations are thus obtained in (M) and (S) separately. Self-diffusion is also discussed. Alternative equations for the mean-square displacement and the non-Gaussian parameter are also derived within MCT approximation. All results in both the systems are compared with those obtained by MCT.     

Mode-coupling theory of the glass transition for colloidal liquids in slit geometry

ABSTRACT

We provide a detailed derivation of the mode-coupling equations for a colloidal liquid confined by two parallel smooth walls. We introduce irreducible memory kernels for the different relaxation channels thereby extending the projection operator technique to colloidal liquids in slit geometry. Investigating both the collective dynamics as well as the tagged-particle motion, we prove that the mode-coupling functional assumes the same form as in the Newtonian case corroborating the universality of the glass-transition singularity with respect to the microscopic dynamics.     

Micro-economic analysis of the physical constrained markets: game theory application to competitive electricity markets

Competition has been introduced in the electricity markets with the goal of reducing prices and improving efficiency. The basic idea which stays behind this choice is that, in competitive markets, a greater quantity of the good is exchanged at a lower price, leading to higher market efficiency. Electricity markets are pretty different from other commodities mainly due to the physical constraints related to the network structure that may impact the market performance. The network structure of the system on which the economic transactions need to be undertaken poses strict physical and operational constraints. Strategic interactions among producers that game the market with the objective of maximizing their producer surplus must be taken into account when modeling competitive electricity markets. The physical constraints, specific of the electricity markets, provide additional opportunity of gaming to the market players. Game theory provides a tool to model such a context. This paper discussed the application of game theory to physical constrained electricity markets with the goal of providing tools for assessing the market performance and pinpointing the critical network constraints that may impact the market efficiency. The basic models of game theory specifically designed to represent the electricity markets will be presented. IEEE30 bus test system of the constrained electricity market will be discussed to show the network impacts on the market performances in presence of strategic bidding behavior of the producers.     

Kinetic theory of vibrational relaxation in a radiation field: The optic-acoustic effect

A microscopic derivation is presented of the rate equations governing vibrational relaxation occurring in the optic-acoustic effect. Detailed expressions applicable to the spectrophone experiment are given both for an excitation source consisting of a broadband radiation field and for laserdriven systems. It is clear from the present treatment that no real advantage accrues from the use of laser excitation sources in the standard spectrophone experiment, due to the resultant strong dependence of the driving force itself on the mechanical chopper frequency. For broadband radiation field the dependence on the chopper frequency is removed and the standard result containing the Einstein coefficient of induced absorption is recovered. The spectrophone response for the simplest case of a two-level system is given explicitly and its similarity to phenomenologically derived expressions is pointed out.The work of F.R.M. was supported in part by a grant from the National Research Council of Canada. The work of A.T. was supported by the Foundation for Fundamental Research on Matter, which is sponsored by the Netherlands Organization for the Advancement of Pure Research.