Cycling Co-Evolution Resulting from Genetic Adaptation in Two-Person Zero-Sum Games

We consider two populations co-evolving with fitness defined by the payoff in a two-person zero-sum game. We show that such situations lead to spontaneous and sustained oscillations iff the optimal strategy of the game is mixed.     

A methodology for missile countermeasures optimization under uncertainty

The missile countermeasures optimization problem is a complex strategy optimization problem that combines aircraft maneuvers with additional countermeasures in an attempt to survive attack from a single surface-launched, anti-aircraft missile. Classic solutions require the evading aircraft to execute specific sequences of maneuvers at precise distances from the pursuing missile and do not effectively account for uncertainty about the type and/or current state of the missile. This paper defines a new methodology for solving the missile countermeasures optimization problem under conditions of uncertainty. The resulting genetic programming system evolves programs that combine maneuvers with such countermeasures as chaff, flares, and jamming to optimize aircraft survivability. This methodology may be generalized to solve strategy optimization problems for intelligent, autonomous agents operating under conditions of uncertainty.     

On the Rate of Convergence of Fictitious Play

Fictitious play is a simple learning algorithm for strategic games that proceeds in rounds. In each round, the players play a best response to a mixed strategy that is given by the empirical frequencies of actions played in previous rounds. There is a close relationship between fictitious play and the Nash equilibria of a game: if the empirical frequencies of fictitious play converge to a strategy profile, this strategy profile is a Nash equilibrium. While fictitious play does not converge in general, it is known to do so for certain restricted classes of games, such as constant-sum games, non-degenerate 2×n games, and potential games. We study the rate of convergence of fictitious play and show that, in all the classes of games mentioned above, fictitious play may require an exponential number of rounds (in the size of the representation of the game) before some equilibrium action is eventually played. In particular, we show the above statement for symmetric constant-sum win-lose-tie games.     

Evolutionarily stable sets in quantum penny flip games

In game theory, an Evolutionarily Stable Set (ES set) is a set of Nash Equilibrium (NE) strategies that give the same payoffs. Similar to an Evolutionarily Stable Strategy (ES strategy), an ES set is also a strict NE. This work investigates the evolutionary stability of classical and quantum strategies in the quantum penny flip games. In particular, we developed an evolutionary game theory model to conduct a series of simulations where a population of mixed classical strategies from the ES set of the game were invaded by quantum strategies. We found that when only one of the two players’ mixed classical strategies were invaded, the results were different. In one case, due to the interference phenomenon of superposition, quantum strategies provided more payoff, hence successfully replaced the mixed classical strategies in the ES set. In the other case, the mixed classical strategies were able to sustain the invasion of quantum strategies and remained in the ES set. Moreover, when both players’ mixed classical strategies were invaded by quantum strategies, a new quantum ES set was emerged. The strategies in the quantum ES set give both players payoff 0, which is the same as the payoff of the strategies in the mixed classical ES set of this game.     

改进信息化武器系统性能的仿真博弈混合方法

用定量分析的方法改进性能是信息化武器系统开发和运用中必须解决的重要问题,借助仿真和博弈分析的混合方法,在对传统混合策略纳什均衡原理应用的基础上,构建基于二人非零和(TPNZS)非合作博弈模型来改进信息化武器系统的性能,对典型信息化武器系统-舰载导弹防空系统的初步研究表明:用识别正确、错误目标能力以及导弹命中目标能力描述的舰载导弹防空系统的最优改进性能策略为△*=(0,△2*,1-△2*)=(0.0000,0.7118,0.2882).     

Fuzzy signaling game of deception between ant-inspired deceptive robots with interactive learning

In this study the robotic deception phenomenon is raised in the framework of a signaling game which utilizes fuzzy logic and game theory along with inspirations from nature. Accomplishing the fuzzy signaling strategy set for deceptive players serves as a great part of our contribution and on this aim, hierarchical fuzzy inference systems support receiver’s actions and sender’s ant-inspired deceptive signals (track and pheromone). In addition, special deceptive robots and visually-supported experimental environment are also provided. The fuzzy behavior of robots defines the strategy type of players. The final result of deception process depends on this strategy type which leads to proposing a payoff matrix in which each cell of mutual costs is defined with special supporting logic related to our deception game with pursuit–evasion applications. Furthermore, motivated by animal signaling, through applying mixed strategies on deceiver’s honesty level and rival’s trust level, the corresponding learning dynamics are investigated and the conceptual discussion put forward serves as a proof to the smart human-like behavior that occurs between the robots: the interactive learning. Simulation results show that robots are capable of interactive learning within deceptive interaction and finally change their strategies to adopt themselves to new situation occurred due to opponent’s strategy change. Because of repetitive change in strategies as a result of learning, the conditions of a persistent deception without breakdown holds for this game where deceiver can frequently benefit from deception without leaving rival to lose its trust totally. The change in strategy will happen after a short time needed to learn the new situation. In rival’s learning process, this short time, which we call the ignorance time, exactly is the period that deceiver can benefit from deception while its evil intends are still concealed. Moreover, in this study an algorithm is given for the proposed signaling game of deception and an illustrative experiment in the introduced experimental environment demonstrates the process of a successful deception. The paper also gives solution to the proposed game by analyzing mixed Nash equilibrium which turns out to be the interior center fixed point of the learning dynamics.     

基于单点多步博弈的网络防御策略选取方法

当前复杂环境下网络安全问题频发,而现有攻防博弈网络防御模型未考虑网络攻击单点多步的特性,无法有效进行网络防御.针对网络攻防实际需求,通过模拟攻防环境和过程,提出一种基于单点多步网络攻防博弈模型的防御策略选取方法.建立单点多步攻防博弈模型,将全局博弈缩小为漏洞上的局部博弈以适应各种防御体系的攻防分析,采用漏洞评分系统量化...     

Cooperative Multiple Pursuers against a Single Evader

This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified.     

Evolutionary collective behavior decomposition model for time series data mining

In this research, we propose a novel framework referred to as collective game behavior decomposition where complex collective behavior is assumed to be generated by aggregation of several groups of agents following different strategies and complexity emerges from collaboration and competition of individuals. The strategy of an agent is modeled by certain simple game theory models with limited information. Genetic algorithms are used to obtain the optimal collective behavior decomposition based on history data. The trained model can be used for collective behavior prediction. For modeling individual behavior, two simple games, the minority game and mixed game are investigated in experiments on the real-world stock prices and foreign-exchange rate. Experimental results are presented to show the effectiveness of the new proposed model.     

一个基于“恶意对抗”的公平交互机制的研究

由于多代理交互环境中检测机制、仲裁机制的有限性,合法代理将注定要遭受损失。针对上述现象,该文提出了一个恶意对抗机制（Malice-Antagonized Interaction Mechanism,MAIM),即在该机制下,交互代理双方都允许表现出恶意行为,以期实现交互的公平性,为了分析MAIM机制的可行性,文中应用游戏理论对MAIM在几种典型的游戏中实现交互公平性的情况进行了分析和证明。最终得出结论：在完善信息的纯策略游戏中,MAIM无法实现交互的公平性,而在完美信息的混合策略游戏、不完美信息的顺序游戏和同时决策游戏中,能实现交互的公平性。从而从理论上证明了恶意对抗机制的可行性。     

Finite-horizon differential games for missile–target interception system using adaptive dynamic programming with input constraints

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton–Jacobi–Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile–target interception system, assuming first-order dynamics for the interceptor and target.     

基于博弈论框架的用户行为决策模型

从风险与安全的角度提出一种新的用户行为决策模型,将服务提供者和用户作为非合作博弈的对立方,在不完全信息静态博弈的基础上研究博弈参与者之间的交互行为。从博弈参与者的相互依赖的行动选择角度建立博弈模型,求出最优混合策略。在此基础上,服务提供者从最大化自己利益的角度作出决策。     

基于博弈论的隐私保护分布式数据挖掘

隐私保护的分布式数据挖掘问题是数据挖掘领域的一个研究热点,而基于经济视角,利用博弈论的方法对隐私保护分布式数据挖掘进行研究只是处于初始阶段。基于收益最大化,研究了完全信息静态博弈下分布式数据挖掘中参与者(两方或多方)的策略决策问题,得出了如下结论:数据挖掘在满足一定的条件下,参与者(两方或多方)的准诚信攻击策略是一个帕累托最优的纳什均衡策略;在准诚信攻击的假设下,参与者(多方)的非共谋策略并不是一个纳什均衡策略。同时给出了该博弈的混合战略纳什均衡,它对隐私保护分布式数据挖掘中参与者的决策具有一定的理论和指导意义。     

On the value of commitment

In game theory, it is well known that being able to commit to a strategy before other players move can be beneficial. In this paper, we analyze how much benefit a player can derive from commitment in various types of games, in a quantitative sense that is similar to concepts such as the value of mediation and the price of anarchy. Specifically, we introduce and study the value of pure commitment (the benefit of committing to a pure strategy), the value of mixed commitment (the benefit of committing to a mixed strategy), and the mixed versus pure commitment ratio (how much can be gained by committing to a mixed strategy rather than a pure one). In addition to theoretical results about how large these values are in the extreme case in various classes of games, we also give average-case results based on randomly drawn normal-form games.     

Evolutionary programming using a mixed mutation strategy

Different mutation operators have been proposed in evolutionary programming, but for each operator there are some types of optimization problems that cannot be solved efficiently. A mixed strategy, integrating several mutation operators into a single algorithm, can overcome this problem. Inspired by evolutionary game theory, this paper presents a mixed strategy evolutionary programming algorithm that employs the Gaussian, Cauchy, Lévy, and single-point mutation operators. The novel algorithm is tested on a set of 22 benchmark problems. The results show that the mixed strategy performs equally well or better than the best of the four pure strategies does, for all of the benchmark problems.     

Best neighbor strategy to enforce cooperation among selfish nodes in wireless ad hoc network

Trust among nodes in a self-organizing network such as a mobile ad hoc network presents a number of problems and paradoxes. One of the challenging characteristics of wireless and mobile ad hoc networks consists in exploring ways to cope up with selfish behavior of neighbors towards network functions such as routing and forwarding. This paper attempts to deal with such mechanisms and as a result it introduces a distinct model to study the behavior of selfish neighbors using strategic, non-cooperative game theory. Many research works have used Tit-For-Tat strategy for analysis when they deploy game theory to stimulate cooperation. A compliant and an adaptable strategy called Best Neighbor Strategy [BNS] is proposed in this paper for the packet forwarding game in a wireless ad hoc environment. The behavior of nodes is probed varying the proportion of selfishness and also the size of the population while forwarding the packets. The investigations have brought out that the proposed cooperation enforcement policy is scalable, is able to converge faster and is robust against selfishness. BNS achieves evolutionary stability even under the invasion of selfish strategy at different proportions. Further, BNS proves to be a pure evolutionary stable strategy as it evolves to dominate the population from whatever the initial frequency it starts with and it totally out-competes the malign behavior shown by selfish strategy, which means that BNS is immune to invaders. The observations and analysis have shown that the ad hoc paradigm can be modeled significantly using an approach, which has been developed for game theory.     

基于网络攻防博弈模型的最优防御策略选取方法

为了降低安全风险损失,并在有限的资源下做出最优网络防御决策,设计了一种网络攻防博弈最优策略选取方法。首先,建立网络攻防博弈模型,证明了该模型混合策略纳什均衡的存在性;然后,给出了基于该模型的网络攻防策略选取算法,包括基于网络攻防策略图的攻防策略搜索算法、攻防双方不同策略下基于通用漏洞评分系统的效用函数量化计算方法和混合策略纳什均衡求解方法等;最后,在一个典型的网络攻防实例场景下对模型的有效性进行了分析和验证。实验结果表明,该模型能够有效地生成最优防御决策方案。     

Pushdown Processes: Games and Model-Checking

A pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condition in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton. An EXPTIME procedure for finding a winner in a pushdown game is presented. The procedure is then used to solve the model-checking problem for the pushdown processes and the propositional μ-calculus. The problem is shown to be DEXPTIME-complete.     

A Differential Game Based Guidance Law for an Accelerating Exoatmospheric Missile

A differential game‐based guidance law design is proposed for a class of accelerating exoatmospheric missiles. By analyzing the nonlinear dynamic equations, a class of motions that does not require maneuver effort is derived for the missile. Using this property, a two phase guidance scheme can be derived that permits a perfect interception. In Phase 1, the missile is put in collision course with the target, which means in Phase 2 the missile should intercept the target with a straight line flight course, at a specified terminal body angle. Differential game based guidance laws are derived respectively for the two phases to guarantee the implementation of the guidance scheme. Simulation results show that the methodology provides robust interception performance.     

优化蚁群算法在反舰导弹航路规划中的应用

应用基本蚁群算法解决反舰导弹航路规划问题,会有收敛速度慢、计算时间长、易于过早陷入局部最优等缺点。针对该问题,引入轮盘式选择策略、精英策略以及路径优化策略对传统蚁群算法进行优化,并将优化算法应用于反舰导弹航路规划中;同时通过对反舰导弹的可行航向进行限定,缩小了航路规划的最大搜索范围。仿真实验表明,基于优化蚁群算法的反舰导弹航路规划不仅缩短了最优航路长度,而且提高了最优航路搜索过程的收敛速度。