Genjiu Xu

A new approach of cooperative interval games: The interval core and Shapley value revisited

Abstract We study the model of cooperative interval games by using Moore’s subtraction operator and an introduced total order with respect to the set of closed intervals. The focus is on two basic solutions for this model, the interval core and the interval Shapley value. By using the new tools, we introduce and study new notions of interval cores and Shapley-like values, discuss relations between them and the existing interval solutions. Axiomatic characterizations of the introduced interval Shapley-like values are given.

A repeated game theoretical approach for clustering in mobile ad hoc networks

In view of energy, mobility and degree of the nodes, a clustering algorithm is proposed which provides an effective method for establishing a hierarchical structure of the mobile ad hoc networks. Moreover, a repeated game model together with limited punishment mechanism is introduced for constraining the selfish nodes that deceive to avoid being cluster-heads to save energy. It is also proved that the profile of acting honestly at each stage of the clustering will deduce the unique Nash Equilibrium of the game. So, with the incentive mechanism, the clustering algorithm will work much more efficiently and stably.

Decoupled Visual Servoing With Fuzzy Q -Learning

The objective of visual servoing aims to control an objects motion with visual feedbacks and becomes popular recently. Problems of complex modeling and instability always exist in visual servoing methods. Moreover, there are few research works on selection of the servoing gain in image-based visual servoing (IBVS) methods. This paper proposes an IBVS method with Q-Learning, where the learning rate is adjusted by a fuzzy system. Meanwhile, a synthetic preprocess is introduced to perform feature extraction. The extraction method is actually a combination of a color-based recognition algorithm and an improved contour-based recognition algorithm. For dealing with underactuated dynamics of the unmanned aerial vehicles (UAVs), a decoupled controller is designed, where the velocity and attitude are decoupled through attenuating the effects of underactuation in roll and pitch and two independent servoing gains, for linear and angular motion servoing, respectively, are designed in place of single servoing gain in traditional methods. For further improvement in convergence and stability, a reinforcement learning method, Q-Learning, is taken for adaptive servoing gain adjustment. The Q-Learning is composed of two independent learning agents for adjusting two serving gains, respectively. In order to improve the performance of the Q-Learning, a fuzzy-based method is proposed for tuning the learning rate. The results of simulations and experiments on control of UAVs demonstrate that the proposed method has better properties in stability and convergence than the competing methods.

Procedural interpretation and associated consistency for the egalitarian Shapley values

An -egalitarian Shapley value is the convex combination of the Shapley value and the equal division value in terms of a social selfish coefficient [0,1] reconciling the two polar opinions of marginalism and egalitarianism. We present a procedural interpretation for every egalitarian Shapley value. We also characterize each -egalitarian Shapley value by associated consistency, continuity and the -dummy player property. The Jordan normal form approach is applied as the pivotal technique to accomplish the most important proof.

Research on self-adaptive decision-making mechanism for competition strategies in robot soccer

In the robot soccer competition platform, the current confrontation decision-making system suffers from difficulties in optimization and adaptability. Therefore, we propose a new self-adaptive decision-making (SADM) strategy. SADM compensates for the restrictions of robot physical movement control by updating the task assignment and role assignment module using situation assessment techniques. It designs a self-adaptive role assignment model that assists the soccer robot in adapting to competition situations similar to how humans adapt in real time. Moreover, it also builds an accurate motion model for the robot in order to improve the competition ability of individual robot soccer. Experimental results show that SADM can adapt quickly and positively to new competition situations and has excellent performance in actual competition.

Axiomatizations and a Noncooperative Interpretation of the α-CIS Value

In economic allocation problems, egalitarianism and marginalism are two major thoughts to distribute the benefits of cooperation. The α-CIS value reconciles the two thoughts in some variable extent by a parameter α ∈ [0, 1]. The α-CIS value is the center of gravity of the corresponding α-imputation set given the α-imputation set is nonempty. From the cooperative perspective, we present several axiomatizations of the α-CIS value using α-individual rationality or α-dummifying player property. Finally, we provide a noncooperative interpretation of the α-CIS value by a bidding mechanism.

Consistency for the additive efficient normalization of semivalues

This paper contributes to consistency for the additive efficient normalization of semivalues. Motivated from the additive efficient normalization of a semivalue being a B-revision of the Shapley value, we introduce the B-reduced game which is an extension of Sobolev’s reduced game. Then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance, symmetry, and B-consistency. Furthermore, by means of the path-independently linear consistency together with the standardness for two-person games, the additive efficient normalization of semivalues is also characterized. Accessorily, the additive efficient normalization of semivalues is directly verified as the linear consistent least square values (see Ruiz et al., 1998).

Transformation of Characteristic Function in Dynamic Games

Abstract The problem of transformation of characteristic function, using a transformation matrix and connected with associated consistency of a solution concept, was investigated for the class of so-called “one-shot” games. The same problem also arises in dynamic games when players move step by step along the cooperative trajectory. In this case the evolution of characteristic function is, in general, unpredictable and may lead to time-inconsistency of a fixed cooperative solution concept. There are different approaches to overcome this problem based on transformation of characteristic function. In this paper, the step-wise transformation is used, which is a generalization of similar transformation of characteristic function for dynamic games with perfect information, and it leads to the time-consistent solution. The general form of such transformation is proposed.

The Family of Ideal Values for Cooperative Games

In view of the nature of pursuing profit, a selfish coefficient function is employed to describe the degrees of selfishness of players in different coalitions, which is the desired rate of return to the worth of coalitions. This function brings in the concept of individual expected reward to every player. Built on different selfish coefficient functions, the family of ideal values can be obtained by minimizing deviations from the individual expected rewards. Then, we show the relationships between the family of ideal values and two other classical families of values: the procedural values and the least square values. For any selfish coefficient function, the corresponding ideal value is characterized by efficiency, linearity, an equal-expectation player property and a nullifying player punishment property, and also interpreted by a dynamic process. As two dual cases in the family of ideal values, the center of gravity of imputation set value and the equal allocation of nonseparable costs value are raised from new axiomatic angles.

The general prenucleolus of n-person cooperative fuzzy games

Abstract In this paper, we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions. For the general prenucleolus, we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess (Sakawa and Nishizaki (1994) [15] ). As a result, we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions, such as the equalizer solution (Molina and Tejada (2002) [5] ) and Shapley function etc. We prove that the least square general prenucleolus minimizing the variance of the resulting player complaints, is the general prenucleolus. Thus, an optimal solution considered from two aspects of the lexicographic order and the least square criterion, is obtained. In addition, several general prenucleoli are proposed in terms of specific situations.