Coalition Formation for Multiple UAVs Cooperative Search and Attack with Communication Constraints in Unknown Environment

A coalition formation algorithm is presented with limited communication ranges and delays in unknown environment,for the performance of multiple heterogeneous unmanned aerial vehicles(UAVs)in cooperative search and attack missions.The mathematic model of coalition formation is built on basis of the minimum attacking time and the minimum coalition size with satisfying resources and simultaneous strikes requirements.A communication protocol based on maximum number of hops is developed to determine the potential coalition members in dynamic network.A multistage sub-optimal coalition formation algorithm(MSOCFA)with polynomial time is established.The performances of MSOCFA and particle swarm optimization(PSO)algorithms are compared in terms of complexity,mission performance and computational time.A complex scenario is deployed to illustrate how the coalitions are formed and validate the feasibility of the MSOCFA.The effect of communication constraints(hop delay and max-hops)on mission performance is studied.The results show that it is beneficial to determine potential coalition members in a wide and deep range over the network in the presence of less delay.However,when the delays are significant,it is more advantageous to determine coalitions from among the immediate neighbors.

Coalition Formation in Weighted Simple-majority Games under Proportional Payoff Allocation Rules

In this paper, we introduce a simple coalition formation game in the environment of bidding, which is a special case of the weighted majority game （WMG）, and is named the weighted simple-majority game （WSMG）. In WSMG, payoff is allocated to the winners proportional to the players powers, which can be measured in various ways. We define a new kind of stability： the counteraction-stability （C-stability）, where any potential deviating players will confront counteractions of the other players. We show that C-stable coalition structures in WSMG always contains a minimal winning coalition of minimum total power. For the variant where powers are measured directly by their weights, we show that it is NP-hard to find a C-stable coalition structure and design a pseudo-polynomial time algorithm. Sensitivity analysis for this variant, which shows many interesting properties, is also done. We also prove that it is NP-hard to compute the Holler-Packel indices in WSMGs, and hence in WMGs as well.

On Aspiration Solutions in Predicting Coalition Formationin Cooperative Games

This paper consists of two parts. The first part introduces the strict aspiration as a new aspiration solution concept, which is provedto be existent for any cooperative game. The second part deals with theunsolved problem put forward by Bennett by showing that there is atleast one payoff which is balanced, partnered and equal gains aspiration.The proof is algebraic and constructive, thus providing an algorithm forfinding such aspirations.

MAV/UAV task coalition phased-formation method

The formation of the manned aerial vehicle/unmanned aerial vehicle(MAV/UAV) task coalition is considered. To reduce the scale of the problem, the formation progress is divided into three phases. For the task clustering phase, the geographical position of tasks is taken into consideration and a cluster method is proposed. For the UAV allocation phase, the UAV requirement for both constrained and unconstrained resources is introduced, and a multi-objective optimal algorithm is proposed to solve the allocation problem. For the MAV allocation phase, the optimal model is firstly constructed and it is decomposed according to the ideal of greed to reduce the time complexity of the algorithm. Based on the above phases, the MAV/UAV task coalition formation method is proposed and the effectiveness and practicability are demonstrated by simulation examples.

On the Coalitional Rationality and the Inverse Problem for Shapley Value and the Semivalues

In cooperative game theory, a central problem is to allocate fairly the win of the grand coalition to the players who agreed to cooperate and form the grand coalition. Such allocations are obtained by means of values, having some fairness properties, expressed in most cases by groups of axioms. In an earlier work, we solved what we called the Inverse Problem for Semivalues, in which the main result was offering an explicit formula providing the set of all games with an a priori given Semivalue, associated with a given weight vector. However, in this set there is an infinite set of games for which the Semivalues are not coalitional rational, perhaps not efficient, so that these are not fair practical solutions of the above fundamental problem. Among the Semivalues, coalitional rational solutions for the Shapley Value and the Banzhaf Value have been given in two more recent works. In the present paper, based upon a general potential basis, relative to Semivalues, for a given game and a given Semivalue, we solve the connected problem: in the Inverse Set, find out a game with the same Semivalue, which is also coalitional rational. Several examples will illustrate the corresponding numerical technique.

On the Coalitional Rationality of the Shapley Value and Other Efficient Values of Cooperative TU Games

In the theory of cooperative transferable utilities games, (TU games), the Efficient Values, that is those which show how the win of the grand coalition is shared by the players, may not be a good solution to give a fair outcome to each player. In an earlier work of the author, the Inverse Problem has been stated and explicitely solved for the Shapley Value and for the Least Square Values. In the present paper, for a given vector, which is the Shapley Value of a game, but it is not coalitional rational, that is it does not belong to the Core of the game, we would like to find out a new game with the Shapley Value equal to the a priori given vector and for which this vector is also in the Core of the game. In other words, in the Inverse Set relative to the Shapley Value, we want to find out a new game, for which the Shapley Value is coalitional rational. The results show how such a game may be obtained, and some examples are illustrating the technique. Moreover, it is shown that beside the original game, there are always other games for which the given vector is not in the Core. The similar problem is solved for the Least Square Values.

The Symmetric Banzhaf Value for Fuzzy Games with a Coalition Structure

In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.

THE GENERALIZED SYMMETRIC COALITIONAL BANZHAF VALUE FOR MULTICHOICE GAMES WITH A COALITION STRUCTURE

With respect to multichoice games with a coalition structure,a coalitional value named the generalized symmetric coalitional Banzhaf value is defined,which is an extension of the Shapley value for multichoice games and the symmetric coalitional Banzhaf value for traditional games with a coalition structure.Two axiomatic systems are established:One is enlightened by the characterizations for the symmetric coalitional Banzhaf value,and the other is inspired by the characterizations for the Banzhaf value.

Multi-task Coalition Parallel Formation Strategy Based on Reinforcement Learning

代理人联盟是代理人协作和合作的一种重要方式。形成一个联盟，代理人能提高他们的能力解决问题并且获得更多的实用程序。在这份报纸，新奇多工联盟平行形成策略被介绍，并且多工联盟形成的过程是一个 Markov 决定过程的结论理论上被证明。而且，学习的加强被用来解决多工联盟平行的代理人行为策略，和这个过程形成被描述。在多工面向的领域，策略罐头有效地并且平行形式多工联盟。

An Axiomatization of Probabilistic Owen Value for Games with Coalition Structure

In the framework of games with coalition structure, we introduce probabilistic Owen value which is an extension of the Owen value and probabilistic Shapley value by considering the situation that not all priori unions are able to cooperate with others. Then we use five axioms of probabilistic efficiency, symmetric within coalitions, symmetric across coalitions applying to unanimity games, strong monotone property and linearity to axiomatize the value.

COOPERATIVE GAMES ON CONVEX GEOMETRIES WITH A COALITION STRUCTURE

This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~

On the Coalitional Rationality and the Egalitarian Nonseparable Contribution

In earlier works we introduced the Inverse Problem, relative to the Shapley Value, then relative to Semivalues. In the explicit representation of the Inverse Set, the solution set of the Inverse Problem, we built a family of games, called the almost null family, in which we determined more recently a game where the Shapley Value and the Egalitarian Allocations are colalitional rational. The Egalitarian Nonseparable Contribution is another value for cooperative transferable utilities games (TU games), showing how to allocate fairly the win of the grand coalition, in case that this has been formed. In the present paper, we solve the similar problem for this new value: given a nonnegative vector representing the Egalitarian Nonseparable Contribution of a TU game, find out a game in which the Egalitarian Nonseparable Contribution is kept the same, but it is colalitional rational. The new game will belong to the family of almost null games in the Inverse Set, relative to the Shapley Value, and it is proved that the threshold of coalitional rationality will be higher than the one for the Shapley Value. The needed previous results are shown in the introduction, the second section is devoted to the main results, while in the last section are discussed remarks and connected problems. Some numerical examples are illustrating the procedure of finding the new game.

Using Computational Intelligence Algorithms to Solve the Coalition Structure Generation Problem in Coalitional Skill Games

Coalitional skill games （CSGs） are a simple model of cooperation in an uncertain environment where each agent has a set of skills that are required to accomplish a variety of tasks and each task requires a set of skills to be completed, but each skill is very hard to be quantified and can only be qualitatively expressed. Thus far, many computational questions surrounding CSGs have been studied. However, to the best of our knowledge, the coalition structure generation problem （CSGP）, as a central issue of CSGs, is extremely challenging and has not been well solved. To this end, two different computational intelligence algorithms are herein evaluated： binary particle swarm optimization （BPSO） and binary differential evolution （BDE）. In particular, we develop the two stochastic search algorithms with two-dimensional binary encoding and corresponding heuristic for individual repairs. After that, we discuss some fundamental properties of the proposed heuristic. Finally, we compare the improved BPSO and BDE with the state-of-the-art algorithms for solving CSGP in CSGs. The experimental results show that our algorithms can find the same near optimal solutions with the existing approaches but take extremely short time, especially under the large problem size.

Coalition Formation of Microgrids with Distributed Energy Resources and Energy Storage in Energy Market

Power grids include entities such as home-microgrids(H-MGs),consumers,and retailers,each of which has a unique and sometimes contradictory objective compared with others while exchanging electricity and heat with other H-MGs.Therefore,there is the need for a smart structure to handle the new situation.This paper proposes a bilevel hierarchical structure for designing and planning distributed energy resources(DERs)and energy storage in H-MGs by considering the demand response(DR).In general,the upper-level structure is based on H-MG generation competition to maximize their individual and/or group income in the process of forming a coalition with other H-MGs.The upper-level problem is decomposed into a set of low-level market clearing problems.Both electricity and heat markets are simultaneously modeled in this paper.DERs,including wind turbines(WTs),combined heat and power(CHP)systems,electric boilers(EBs),electric heat pumps(EHPs),and electric energy storage systems,participate in the electricity markets.In addition,CHP systems,gas boilers(GBs),EBs,EHPs,solar thermal panels,and thermal energy storage systems participate in the heat market.Results show that the formation of a coalition among H-MGs present in one grid will not only have a significant effect on programming and regulating the value of the power generated by the generation resources,but also impact the demand consumption and behavior of consumers participating in the DR program with a cheaper market clearing price.

Optimization of energy exchange in microgrid networks: a coalition formation approach

In this paper, we elaborate a new strategy based on cooperative game theory models to encourage and manage the interactions in a MicroGrid network. The proposed strategy optimizes the cooperation and the energy exchange in a distributed μGrid network. The strategy consists of a two stage algorithm: Coalition formation algorithm which was specifically created to approximate the optimal set of coalitions that return considerable savings. And the Matching game to manage the energy exchange inside each coalition. The performance of our strategy was verified through simulations. These latter show that the losses can be considerably decreased by the use of the proposed strategy: the rate of the loss reduction can reach up to 20% if the two stages are applied on the network. Moreover, the strategy proved to have a fast convergence which makes it operational for real implemented networks.

Strategically supported cooperation in dynamic games with coalition structures

The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments.From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.

Coalition formation based on a task-oriented collaborative ability vector

Coalition formation is an important coordination problem in multi-agent systems, and a proper description of collaborative abilities for agents is the basic and key precondition in handling this problem. In this paper, a model of task-oriented collaborative abilities is established, where five task-oriented abilities are extracted to form a collaborative ability vector. A task demand vector is also described. In addition, a method of coalition formation with stochastic mechanism is proposed to reduce excessive competitions. An artificial intelligent algorithm is proposed to compensate for the difference between the expected and actual task requirements, which could improve the cognitive capabilities of agents for human commands. Simulations show the effectiveness of the proposed model and the distributed artificial intelligent algorithm.

Cooperative coalition for formation flight scheduling based on incomplete information

This study analyzes the cooperative coalition problem for formation scheduling based on incomplete information. A multi-agent cooperative coalition framework is developed to optimize the formation scheduling problem in a decentralized manner. The social class differentiation mech- anism and role-assuming mechanism are incorporated into the framework, which, in turn, ensures that the multi-agent system （MAS） evolves in the optimal direction. Moreover, a further differen- tiation pressure can be achieved to help MAS escape from local optima. A Bayesian coalition nego- tiation algorithm is constructed, within which the Harsanyi transformation is introduced to transform the coalition problem based on incomplete information to the Bayesian-equivalent coali- tion problem based on imperfect information. The simulation results suggest that the distribution of agents＇ expectations of other agents＇ unknown information approximates to the true distribution after a finite set of generations. The comparisons indicate that the MAS cooperative coalition algo- rithm produces a significantly better utility and possesses a more effective capability of escaping from local optima than the proposal-engaged marriage algorithm and the Simulated Annealing algorithm.

ZS-VALUE FOR RANDOM COALITION GAMES

Ⅰ. INTRODUCTION One has proposed the solutions for n-person coalition games. J. von Neumann and O. Morgenstern found the stable set of the game in 1944. Gillies gave the definition of the core c(v) of the game in 1955. But up to now, in general, there is no criterion for the existence of a core or a stable set, so Shapley defined

Convex linear generalization of random coalition games

The solution of convex linear combinational game of the random coalition games on the ZS-Axiom is given. With this solution, the scale of the solution to combinational game and the scale of convex linear combinational game under certain circumstances are widened.