Nonwmmetric Shapley values for coalitional form games with transferable utility are studied. The nonsymmetries are modeled through nonsymmetric weight systems defined on the players of the games. It is shown axiomatically that two families of solutions of this type are possible. These families are strongly related to each other through the duality relationship on games. While the first family lends itself to applications of nonsymmetric revenue sharing problems the second family is suitable for applications of cost allocation problems. The intersection of these two families consists essentially of the symmetric Shapley value. These families are also char- acterized by a prObabilistic arrival time to the game approach. It is also demonstrated that lack of symmetries may arise naturally when players in a game represent nonequal size constituencies.

On Weighted Shapley Values

Purpose




The purpose of this paper is to propose a layered adjustable autonomy (LAA) as a dynamically adjustable autonomy model for a multi-agent system. It is mainly used to efficiently manage humans’ and agents’ shared control of autonomous systems and maintain humans’ global control over the agents.




Design/methodology/approach




The authors apply the LAA model in an agent-based autonomous unmanned aerial vehicle (UAV) system. The UAV system implementation consists of two parts: software and hardware. The software part represents the controller and the cognitive, and the hardware represents the computing machinery and the actuator of the UAV system. The UAV system performs three experimental scenarios of dance, surveillance and search missions. The selected scenarios demonstrate different behaviors in order to create a suitable test plan and ensure significant results.




Findings




The results of the UAV system tests prove that segregating the autonomy of a system as multi-dimensional and adjustable layers enables humans and/or agents to perform actions at convenient autonomy levels. Hence, reducing the adjustable autonomy drawbacks of constraining the autonomy of the agents, increasing humans’ workload and exposing the system to disturbances.




Originality/value




The application of the LAA model in a UAV manifests the significance of implementing dynamic adjustable autonomy. Assessing the autonomy within three phases of agents run cycle (task-selection, actions-selection and actions-execution) is an original idea that aims to direct agents’ autonomy toward performance competency. The agents’ abilities are well exploited when an incompetent agent switches with a more competent one.

Formulating layered adjustable autonomy for unmanned aerial vehicles

Multi-objective linear programming games and applications in supply chain competition

Purpose




The purpose of this paper is to deal with profit maximization problem of two-layer supply chain (SC) under fuzzy stochastic demand having finite mean and unknown variance. Buyback policy is employed from the retailer to supplier. The profit of the supplier solely depends on the order size of the retailers. However, the loss of shortage items is related to loss of profit and goodwill dependent. The authors develop the profit function separately for both the retailer and supplier, first, for a decentralized system and, second, joining them, the authors get a centralized system (CS) of decision making, in which one is giving more profit to both of them. The problem is solved analytically first, then the authors fuzzify the model and solve by fuzzy Hausdorff distance method.




Design/methodology/approach




The analytical models are formed for both centralized and decentralized systems under non-cooperative and cooperative environment with suitable constraints. A significant assumption on density function, namely Cauchy-type density function, is introduced for demand rate because of its wider range of the retailers’ satisfactions. Fuzzy Hausdorff metric is incorporated within the fuzzy components of the fuzzy sets itself. Using this method, the authors find out closure values of both centralized and decentralized policies, which is an essential part of any cooperative and non-cooperative two-layer SC models. Moreover, the authors take care of the profit values with corresponding ambiguities for both the systems explicitly.




Findings




It is found that the centralize policy of SC could only be able to maximize the profit of both the retailers and suppliers. All analytical results are illustrated numerically along with sensitivity analysis and side by side comparative studies between Hausdorff and Euclidean distance measure are done exclusively.




Research limitations/implications




The main focus of attention of the proposed model is given to usefulness of Hausdorff distance. Unlike other distances, Hausdorff distance can take special care on the similarity measures of different fuzzy sets. Researchers have been engaged to use Hausdorff distance on the different fuzzy sets but, in this study, the authors have used it within the components of a same fuzzy set to gain more closure values than other methods.




Originality/value




The use of this Hausdorff distance approach is totally new as per literature survey suggested yet. However, the Cauchy-type density function has not been introduced anywhere in SC management problems by modern researchers still now. In crisp model, the sensitivity on goodwill measures really provides a special attention also.

Two-layer supply chain model for Cauchy-type stochastic demand under fuzzy environment

Multiagent systems (MASs) are usually applied with agents classified into leaders and followers, where selecting appropriate leaders is an important issue for formation control applications. In this paper, we investigate two leader selection problems in second-order MAS, namely, the problem of choosing up to a given number of leaders to minimize the formation error and the problem of choosing the minimum number of leaders to achieve a tolerated level of error. We propose a game theoretical method to address them. Specifically, we design a supermodular game for the leader selection problems and theoretically prove its supermodularity. In order to reach Nash equilibrium of the game, we propose strategies for the agents to learn to select leaders based on stochastic fictitious play. Extensive simulation results demonstrate that our method outperforms existing ones.

Leader Selection via Supermodular Game for Formation Control in Multiagent Systems

Purpose




The paper aims to build the connections between game theory and the resource allocation problem with general uncertainty. It proposes modeling the distributed resource allocation problem by Bayesian game. During this paper, three basic kinds of uncertainties are discussed. Therefore, the purpose of this paper is to build the connections between game theory and the resource allocation problem with general uncertainty.




Design/methodology/approach




In this paper, the Bayesian game is proposed for modeling the resource allocation problem with uncertainty. The basic game theoretical model contains three parts: agents, utility function, and decision-making process. Therefore, the probabilistic weighted Shapley value (WSV) is applied to design the utility function of the agents. For achieving the Bayesian Nash equilibrium point, the rational learning method is introduced for optimizing the decision-making process of the agents.




Findings




The paper provides empirical insights about how the game theoretical model deals with the resource allocation problem uncertainty. A probabilistic WSV function was proposed to design the utility function of agents. Moreover, the rational learning was used to optimize the decision-making process of agents for achieving Bayesian Nash equilibrium point. By comparing with the models with full information, the simulation results illustrated the effectiveness of the Bayesian game theoretical methods for the resource allocation problem under uncertainty.




Originality/value




This paper designs a Bayesian theoretical model for the resource allocation problem under uncertainty. The relationships between the Bayesian game and the resource allocation problem are discussed.

Fang Yu

Papers

A game theoretical approach for distributed resource allocation with uncertainty