基于演化博弈惩罚机制的多智能体协作稳定性研究

针对复杂、动态环境中多Agent协作的稳定性问题,提出了一种基于博弈论及惩罚机制的协作方法,通过效用函数来选择最优策略,实现均衡协作;为了提高协作的稳定性与成功率,引入惩罚机制,通过不断调整惩罚系数来维护多Agent协作的稳定性,并在形成协作团队时,充分考虑参与协作的Agent的信誉值。仿真结果表明,该方法能有效地降低任务完成时间,避免Agent在动态协作中随意退出,提高协作效率及协作稳定性。     

Dynamics in network interaction games

We study the convergence times of dynamics in games involving graphical relationships of players. Our model of interaction games generalizes a variety of recently studied games in game theory and distributed computing. In a local interaction games each agent is a node embedded in a graph and plays the same 2-player game with each neighbor. He can choose his strategy only once and must apply his choice in each 2-player game he is involved in. This represents a fundamental model of decision making with local interaction and distributed control. Furthermore, we introduce a generalization called 2-type interaction games, in which one 2-player game is played on edges and possibly another game is played on non-edges. For the popular case with symmetric 2 ×?2 games, we show that several dynamics converge to a pure Nash equilibrium in polynomial time. This includes arbitrary sequential better-response dynamics, as well as concurrent dynamics resulting from a distributed protocol that does not rely on global knowledge. We supplement these results with an experimental comparison of sequential and concurrent dynamics.     

Semi-tensor product approach to networked evolutionary games

In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs.
To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.     

On finite potential games

A linear system, called the potential equation (PE), is presented. It is proved that a finite game is potential if and only if its potential equation has solution. Some properties of the potential equation are obtained. Based on these properties, a closed form solution of the PE is obtained. Moreover, a formula based on the solution of the PE is obtained to calculate the potential function. Finally, it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential. Some interesting examples are presented to illustrate the theoretical results.     

Linear-quadratic discrete-time dynamic potential games

Discrete-time game-theoretic models of resource exploitation are treated as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim of the paper is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadratic form is identified. As an example, the dynamic game of bioresource management is considered and the potentials are constructed in the case of symmetric and asymmetric players.     

Modelling and strategy consensus for a class of networked evolutionary games

Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy consensus for a class of networked evolutionary games (NEGs) with ‘unconditional imitation updating rule’, and presents a number of new results. First, the given NEG is converted to an algebraic form via the semi-tensor product method, and an algorithm is established to obtain the algebraic expression of the considered game. Second, based on the algebraic form, the behaviours of the players in the given evolutionary games are analysed, and some meaningful results are presented. Finally, the strategy consensus problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to make the given NEG reach strategy consensus. The study of an illustrative example shows that the new results obtained in this paper work very well.     

N人合作博弈的Nash及演化均衡稳定策略分析

在有限理性的基础上,对N人合作博弈的对称Nash均衡进行了分析,并引入演化博弈理论分析了参与人的演化均衡稳定策略,得到了不同策略选择下的均衡点。进而应用生物复制动态理论对离散时间及连续时间下的复制动态稳定集进行了研究。最后通过实例说明了该方法在博弈均衡选择上的有效性。     

Finite element approach to continuous potential games

Dear editor, The concept of potential games was proposed for the first time by Rosenthal in 1973 [1].The seminal study by Monderer and Shapley [2] presented sys...     

Crossover and evolutionary stability in the prisoner's dilemma

We examine the role played by crossover in a series of genetic algorithm-based evolutionary simulations of the iterated prisoner's dilemma. The simulations are characterized by extended periods of stability, during which evolutionarily meta-stable strategies remain more or less fixed in the population, interrupted by transient, unstable episodes triggered by the appearance of adaptively targeted predators. This leads to a global evolutionary pattern whereby the population shifts from one of a few evolutionarily metastable strategies to another to evade emerging predator strategies. While crossover is not particularly helpful in producing better average scores, it markedly enhances overall evolutionary stability. We show that crossover achieves this by (1) impeding the appearance and spread of targeted predator strategies during stable phases, and (2) greatly reducing the duration of unstable epochs, presumably by efficient recombination of building blocks to rediscover prior metastable strategies. We also speculate that during stable phases, crossover's operation on the persistently heterogeneous gene pool enhances the survival of useful building blocks, thus sustaining long-range temporal correlations in the evolving population. Empirical support for this conjecture is found in the extended tails of probability distribution functions for stable phase lifetimes.     

Dynamics and stability of a delay-locked loop

We discuss the transient behavior of a delay-locked loop which is designed to generate a delay-error signal that is proportional to the difference in the autocorrelation function of the input signal at two points separated by a fixed time2tau_{1}. When the input signal is a sine wave, we present an exact solution which shows that the system is stable and achieves a delay lock with an ambiguity of an integral number of periods. The second input considered is that of a stationary, ergodic, and band-limited Gaussian signal. In this case we present an approximate analysis which predicts that for times long compared to the inverse bandwidth of the random signal that the delay error is log-normally distributed. For this case we develop the almost sure sample stability criterion [1]. When this criterion is met, the system sample solutions are stable with probability one independant of the system amplification. We also develop stability criteria which limit the system amplification for stability of the first and second moments of the time delay.     

Strategic stability in linear-quadratic differential games with nontransferable payoffs

We address the problem of strategically supported cooperation for linear-quadratic differential games with nontransferable payoffs. As an optimality principle, we study Pareto-optimal solutions. It is assumed that players use a payoff distribution procedure guaranteeing individual rationality of a cooperative solution over the entire game horizon. We prove that under these conditions a Pareto-optimal solution can be strategically supported by an ε-Nash equilibrium. An example is considered.     

Dynamics of neural populations: stability and synchrony

A population formulation of neuronal activity is employed to study an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion for the critical gain at which time asynchronous behavior becomes unstable. At instability the dynamics can undergo a supercritical Hopf bifurcation and the population passes to a synchronous state. Under different conditions it can pass to synchrony through a subcritical Hopf bifurcation. And at high gain a network can reach a runaway state, in finite time, after which the network no longer supports bounded solutions.The introduction of time delayed feedback leads to a rich range of phenomena. For example, for a given external input, increasing gain produces transition from asynchrony, to synchrony, to asynchrony and finally can lead to divergence. Time delay is also shown to strongly mollify the amplitude of synchronous oscillations. Perhaps, of general importance, is the result that synchronous behavior can exist only for a narrow range of time delays, which range is an order of magnitude smaller than periods of oscillation.     

Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method

Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of evolutionary networked games with “myopic best response adjustment” rule, and presents a number of new results. First, the dynamics of the evolutionary networked game is converted to an algebraic form via the semi-tensor product, and an algorithm is established to construct the algebraic formulation for the game. Second, based on the algebraic form, the dynamical behavior of evolutionary networked games is discussed, and some interesting results are presented. Finally, the strategy optimization problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to maximize the average payoff of the pseudo-player. The study of an illustrative example shows that the new results obtained in this paper work very well.     

Dynamics and stability of plane trusses with gusset plates

The effect of gusset plates on free and forced vibration and stability analyses of plane trusses is investigated. The gusset plates are considered to be finite joints possessing mass and rotational flexibility. The bars of the truss are assumed to be elastic Bernoulli-Euler beams with distributed mass. Axial deformation of the bars and the effect of a constant axial force on the bending stiffness are taken into account. On the basis of these assumptions element stiffness matrices are constructed and presented in detail. The general formulation and solution of stability and free and forced vibration problems of trusses is discussed. Examples are presented in detail which demonstrate the effect of the gusset plates on the behavior of trusses under static or dynamic loads.     

Dynamics of fitness sharing evolutionary algorithms for coevolution of multiple species

This paper builds the normal model of fitness sharing with proportionate selection on real-valued functions, and derives the dynamic formula to describe the evolution process of the population with the fitness sharing. The normal modeling simulation is investigated on specific test functions, and experimental results illustrate that the normal model is able to describe exactly the dynamics of the fitness sharing EAs and is a good platform to study the behavior of the fitness sharing EAs with regard to niching radius. The experimental results of the normal modeling simulation and the fitness sharing EAs verify the dilemma in finding optimal niche radius to achieve both good niching convergence and niching efficiency, for which a hybrid scheme is proposed to carry out the niching task.     

Analysing stability and investments in railway networks using advanced evolutionary algorithms

We consider a network of periodically running railway lines. Investments are possible to increase the speed and to improve the synchronisation of trains. The model also includes random delays of trains and the propagation of delays across the network. We derive a cost‐benefit analysis of investments, where the benefit is measured in reduced waiting time for passengers changing lines. We also estimate the actual mean waiting time simulating the train delays. This allows us to analyse the impact that an increasing synchronisation of the timetable has on its stability. Simulation is based on an analytical model obtained from queueing theory. We use sophisticated adaptive evolutionary algorithms, which send off avant‐garde solutions from time to time to speed up the optimisation process. As there is a high correlation between scheduled and estimated waiting times for badly synchronised timetables, we are even able to include the time consuming simulation into our optimisation runs.     

An evolutionary tuned driving system for virtual car racing games: The AUTOPIA driver

This work presents a driving system designed for virtual racing situations. It is based on a complete modular architecture capable of automatically driving a car along a track with or without opponents. The architecture is composed of intuitive modules, with each one being responsible for a basic aspect of car driving. Moreover, this modularity of the architecture will allow us to replace or add modules in the future as a way to enhance particular features of particular situations. In the present work, some of the modules are implemented by means of hand‐designed driving heuristics, whereas modules responsible for adapting the speed and direction of the vehicle to the track's shape, both critical aspects of driving a vehicle, are optimized by means of a genetic algorithm that evaluates the performance of the controller in four different tracks to obtain the best controller in a large number of situations; the algorithm also penalizes controllers that go out of the track, lose control, or get damaged. The evaluation of the performance is done in two ways. First, in runs with and without adversaries over several tracks. And second, the architecture was submitted as a participant to the 2010 Simulated Car Racing Competition, which in end won laurels. © 2012 Wiley Periodicals, Inc.     

Modelling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism

This paper investigates the evolutionary dynamic and strategy optimisation for a kind of networked evolutionary games whose strategy updating rules incorporate ‘bankruptcy’ mechanism, and the situation that each player's bankruptcy is due to the previous continuous low profits gaining from the game is considered. First, by using semi-tensor product of matrices method, the evolutionary dynamic of this kind of games is expressed as a higher order logical dynamic system and then converted into its algebraic form, based on which, the evolutionary dynamic of the given games can be discussed. Second, the strategy optimisation problem is investigated, and some free-type control sequences are designed to maximise the total payoff of the whole game. Finally, an illustrative example is given to show that our new results are very effective.     

Analyzing the evolutionary stability of the vendor-managed inventory supply chains

One of the widely used strategies for achieving system integration in the arena of supply chain management is the vendor-managed inventory (VMI) approach. Although there exists a large amount of literature that examines various aspects of VMI, little looks at how this model evolves as the implementation progresses and matures. Therefore, this paper shows how to analyze the intrinsic evolutionary mechanism of the VMI supply chains by applying the evolutionary game theories. It is found that during the early stage of the VMI implementation, the upstream supplier will have some profit loss; however, as the transaction quantity increases in the long run, which will eventually benefit the entire chain, it is necessary for the downstream buyer to share profit with the upstream supplier to cover the supplier’s initial loss in order to exploit and sustain the benefits of the VMI. Additionally, the impact factors for VMI to become an evolutionary stable strategy are examined. All the results identify the conditions under which the VMI model is favorable over the traditional chain structure and shed lights on when and why collaboration is critical for a successful, long-term implementation of VMI.