INFLUENCE OF ENVIRONMENTAL CHANGES ON COOPERATIVE BEHAVIOR IN THE PRISONER'S DILEMMA GAME ON AN ARTIFICIAL SOCIAL MODEL

In this paper, by simulations on an artificial social model, we analyze cooperative behavior of agents playing the prisoner's dilemma game, in which each of the agents has the two strategies: cooperate and defect. Because defect yields a better payoff whichever strategy an opponent chooses, it is rational for an agent to choose defect in a single game or a finite number of games. However, it is known that a pair of cooperates can also be a Nash equilibrium pair if the players do not know when the game is over or the game is infinitely repeated. To investigate such cooperative behavior, we employ an artificial social model called the Sugarscape and carry out simulations on the model. Arranging three kinds of environments in the Sugarscape, we examine cooperative behavior of agents who are essentially selfish, in a sense that they maximize their payoffs, and investigate influence of environmental changes on the cooperative behavior.     

Matrix games with missing,interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.     

复杂三维多面体环境中空地协作追逃问题

结合无人机(UAV)的空中移动和无人车(UGV)的地面移动特点,本文提出了一种UAV/UGV空地协作系统,并且针对其在复杂地形中的追逃问题,提出了一种复杂三维多面体环境中UAV/UGV空地协作追逃策略.首先介绍了UAV/UGV空地协作系统的结构与协作追逃问题描述.接着将边界值问题(BVP)改进并离散化作为博弈走法生成器.然后,针对逃方已知追方位置,而追方只具备直线视野(LOS)的不利条件,分析了最坏情况.逃方策略在保证最大生存条件下尽可能获得博弈胜利.追方策略根据逃方状态分成3种情况进行讨论:逃方处于追方的视野范围内、逃方刚刚消失于追方视野以及追方完全丢失逃方的情况.最后,对比仿真结果说明了本文算法的有效性,并分析了追逃结果的影响因素.由于地形是非凸的并且充满障碍,因此该策略虽不能保证追方一定能够胜利,但在最坏情况下是最优的.     

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.     

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.     

Multi-objective design method based on evolution game and its application for suspension

Through research and bionics of biology survival mode, game players with competition, cooperation and self-adaptation capacity are introduced in the multi-objective design. The dynamic behavior and bounded rationality in game processes for players are considered according to Chinese saying “In success, commit oneself to the welfare of the society; in distress, maintain one’s own integrity”. An evolution rule, Poor-Competition-Rich-Cooperation (short for PCRC), is proposed. Then, the corresponding payoff functions of competition and cooperation behavior are established and a multi-objective design method based on evolution game is proposed. The calculation steps are as follows: 1) Taking the design objectives as different game players, and calculating factors of the design variables to objective and fuzzy clustering. The design variables are divided into multiple strategy subsets owned by each game player. 2) According to the evolution rule, each player determines its behavior and payoff function in this game round. 3) In their own strategy subsets, each game player takes their payoff as mono-objective for optimization. It gives the best strategy upon other players. And so the best strategies of all players conform the group strategy in this round. The final equilibrium solution is obtained through multi-round game based on convergence criterion. The validity and reliability of this method are shown by the results of an example of a tri-objective optimization design of passive suspension parameters.     

基于纳什均衡博弈的多无人机对地攻击目标分配方法

研究一种新的多无人机对地攻击目标分配问题.该问题中攻击方试图通过无人机击毁防御方的高价值目标,防御方试图通过发射拦截导弹对无人机进行拦截,但攻防双方无法事先观察到对方实际采取的目标分配方案.通过分析防御方的拦截导弹目标分配方案对攻击方收益的影响,将问题构建为一个零和矩阵博弈模型,模型的策略空间随无人机、高价值目标、拦截导弹数量的增加呈爆炸式增长.鉴于此,现有算法难以在有效时间内对其进行求解,提出一种基于两阶段邻域搜索的改进Double Oracle (DO-TSNS)算法.实验结果表明,相较于DO、UWMA和DO-NS算法, DO-TSNS算法能够更有效地求解考虑防御方具有拦截行为的多无人机对地攻击目标分配问题.     

面向无人机自主防碰撞的认知博弈制导控制

针对非隔离空域中的无人机碰撞规避问题,提出一种基于认知博弈制导的无人机自主防碰撞方法.首先,描述了非隔离空域中无人机自主防碰撞控制问题.其次,建立了无人机与入侵机的运动学模型,并构建了无人机的认知安全域,将无人机碰撞规避问题转化为涉及两方的博弈问题.然后,提出了制导策略集的求解方法.最后,仿真结果验证了所提方法的有效性.     

Tropical linear-fractional programming and parametric mean payoff games

Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties (involving the value of the game and its derivative) that we characterize combinatorially. We use this idea to design a Newton-like algorithm to solve tropical linear-fractional programming problems, by reduction to a sequence of auxiliary mean payoff game problems.     

A game theoretical perspective on the quantum probabilities associated with a GHZ state

In the standard approach to quantum games, players’ strategic moves are local unitary transformations on an entangled state that is subsequently measured. Players’ payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein–Podolsky–Rosen (EPR) experiment that depends on three players’ directional choices in the experiment. We define the players’ strategic moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment.     

Equilibria and Compromises in Two-Person Zero-Sum Multicriteria Games

Journal of Computer and Systems Sciences International - The problem is to formalize the solution of a two-person zero-sum multicriteria (MC) game, providing a payoff to both players with respect...     

Equilibria problems on games: Complexity versus succinctness

We study the computational complexity of problems involving equilibria in strategic games and in perfect information extensive games when the number of players is large. We consider, among others, the problems of deciding the existence of a pure Nash equilibrium in strategic games or deciding the existence of a pure Nash or a subgame perfect Nash equilibrium with a given payoff in finite perfect information extensive games. We address the fundamental question of how can we represent a game with a large number of players? We propose three ways of representing a game with different degrees of succinctness for the components of the game. For perfect information extensive games we show that when the number of moves of each player is large and the input game is represented succinctly these problems are PSPACE-complete. In contraposition, when the game is described explicitly by means of its associated tree all these problems are decidable in polynomial time. For strategic games we show that the complexity of deciding the existence of a pure Nash equilibrium depends on the succinctness of the game representation and then on the size of the action sets. In particular we show that it is NP-complete, when the number of players is large and the number of actions for each player is constant, and that the problem is -complete when the number of players is a constant and the size of the action sets is exponential in the size of the game representation. Again when the game is described explicitly the problem is decidable in polynomial time.     

Coalition-hierarchical game under uncertainty conditions

An optimization problem in a coalition-hierarchical game under uncertainty conditions is formulated. In the game, information assumptions are that the player of the high hierarchical level (controlling Center) and each low-level coalition estimates uncertainty in its own way. The Center constructs its strategy from the maximum condition for its own payoff function and its minimum in uncertainty. The relationships between coalitions are built upon the guaranteeing absolute active equilibrium understood in the sense of providing the players with guaranteed payoff under the actual uncertainty. The guaranteed uncertainty is obtained with the help of Slater principle. The total equilibrium in the game is called CH-equilibrium. For a quadratic game version, sufficient optimality conditions are obtained. A numerical procedure for solving the game is described and an example is given.     

A discrete-time bioresource management problem with asymmetric players

This paper explores the discrete-time game-theoretic model associated with a bioresource management problem (fish catching). The game engages players (countries or fishing firms) that harvest fish stocks on the infinite horizon. The paper aims at defining the cooperative payoff under different discount factors of the players. We propose applying a Nash bargaining solution for constructing the cooperative strategies of the players. The analysis covers two bargaining schemes, namely, the one for the whole duration of the game and the recursive bargaining procedure.     

Interactive strategy sets in multiple payoff games

In game theory, it is usually assumed that each player has only one payoff function and the strategy set of the game is composed of the topological product of individual players’ strategy sets. In real business and system design or control problems, however, players’ strategy sets may be interactive and each player may have more than one payoff function. This paper, investigates the more general situation of multiple payoff and multiple person games in a normal form. In this paper, each player has several payoff functions which are dominated by certain convex cones, and the feasible strategy set of each player may be interactive with those of the other players. This new model is applied to a classical example without requiring variational and quasi-variational inequalities, or point-to-set mappings.     

A Quantum Treatment of Public Goods Economics

Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is difficult to implement, especially if the states must be communicated over some distance. This paper describes a quantum approach to the economically significant n-player public goods game that requires only two-particle entanglement and is thus much easier to implement than more general quantum mechanisms. In spite of the large temptation to free ride on the efforts of others in the original game, two-particle entanglement is sufficient to give near optimal expected payoff when players use a simple mixed strategy for which no player can benefit by making different choices. This mechanism can also address some heterogeneous preferences among the players. PACS: 03.67-a; 02.50Le; 89.65.Gh     

Influence of initial conditions in 2\times 2 symmetric games

It is known that quantum game is characterized by the payoff matrix as well as initial states of the quantum objects used as carriers of information in a game. Further, the initial conditions of the quantum states influence the strategies adopted by the quantum players. In this paper, we identify the necessary condition on the initial states of quantum objects for converting symmetric games into potential games, in which the players acquire the same payoff matrix. The necessary condition to preserve the symmetric type and potential type of the game is found to be the same. The present work emphasizes the influence of the initial states in the quantization of games.     

Hierarchical Nash equilibrium seeking strategies of quadratic time-varying games with Euler–Lagrange players

This article investigates the distributed Nash equilibrium seeking problem of quadratic time-varying games with Euler–Lagrange (EL) players, where external disturbances and parametric uncertainties are involved. A gradient-based hierarchical algorithm consisting of a game layer and a control layer is proposed. Specifically, in the game layer, EL players communicate with neighbors through a graph to reach the consensus on potential aggregate values, which will be employed to calculate the gradient of each player's objective function, and then, a gradient-based sliding mode controller is developed to track time-varying gradient in the control layer. Thus, the convergence results are hierarchically obtained through the Lyapunov stability method. In addition, the hierarchical control strategy is extended to address the constrained problems through the utilization of a smooth penalty function. By appropriately choosing control parameters, the Nash equilibrium seeking errors can be arbitrarily small. The relation between the optimal solutions of the original problem and the dual one is further discussed. Finally, the proposed methods are numerically verified.     

Quantum games and quaternionic strategies

It is well-known that the phenomenon of entanglement plays a fundamental role in quantum game theory. Occasionally, games constructed via maximally entangled initial states (MEIS) will have new Nash equilibria yielding to the players higher payoffs than the ones they receive in the classical version of the game. When examining these new games for Nash equilibrium payoffs, a fundamental question arises; does a suitable choice of an MEIS improve the lot of the players? In this paper, we show that the answer to this question is yes for at least the case of a variant of the well-known two player, two strategy game of Chicken. To that end, we generalize Landsburg’s quaternionic representation of the payoff function of two player, two strategy maximally entangled states to games where the initial state is chosen arbitrarily from a circle of maximally entangled initial states and for the corresponding quantized games show the existence of superior Nash equilibrium payoffs when an MEIS is appropriately chosen.     

仿鹰鸽捕食逃逸行为的多无人机分组对抗博弈方法

针对多无人机对抗问题, 本文提出了一种三维空间中仿鹰鸽捕食逃逸行为的多无人机分组对抗博弈方法.在分析鹰鸽捕食逃逸行为的基础上, 文章构建了多无人机博弈对抗系统模型, 并定义了微分博弈中的连续可微值函数, 证明了值函数满足Hamilton-Jacobi-Isaacs(HJI)方程, 从而保证鞍点策略存在. 使用最优分配方法, 为仿鹰无人机一方设计了分组对抗分配策略, 以解决多无人机追逃场景中的任务分配问题. 本文对比仿真实验结果验证了所提出方法的有效性.