Stable Coalition Structure Research Articles

Self-Enforcing Agreements Under Unequal Nationally Determined Contributions

For a large global economy, containing at least 195 nations, with normal goods, and an unequal world income distribution, we consider the endogenous formation and stability of an international environmental agreement (IEA) under nationally determined contributions (NDCs). Nations share green R&D efforts and enjoy R&D spillovers if they join an IEA. Nonmembers do not enjoy R&D spillovers. We show that the Grand Coalition is stable under NDCs if all nations are active carbon abatement and R&D contributors. If some nations are inactive, because they lack sufficient income to provide carbon abatement and R&D, the stable coalition under NDCs is the coalition of all active (wealthier) nations. For comparison purposes, we also show that if IEAs are subject to collectively determined contributions, the stable coalition structure is the stand-alone one.

A Coalitional Game Theoretic Outlook on Distributed Adaptive Parameter Estimation

In this paper, the parameter estimation problem based on diffusion least-mean-squares strategies is analyzed from a coalitional game theoretical perspective. Specifically, while selfishly minimizing only their own mean-square costs, the nodes in a network form coalitions that benefit them. Due to its nature, the problem is modeled as a nontransferable game and two scenarios are studied, one where each node's payoff includes only a suitable estimation accuracy criterion and another one in which a graph-based communication cost is also considered. In the former scenario, we first analyze the nonemptiness of the core of the games corresponding to traditional diffusion strategies, and then, the analysis is extended to a recently proposed node-specific parameter estimation setting where the nodes have overlapped but different estimation interests. In the latter scenario, after formulating a coalitional graph game and providing sufficient conditions for its core nonemptiness, we propose a distributed graph formation algorithm, based on merge-and-split approach, which converges to a stable coalition structure.

Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre and Post Brexit Context

In this paper we apply the so-called partition function approach to study coalition formation in the North-east Atlantic mackerel fishery in the presence of externalities. Atlantic mackerel is mainly exploited by the European Union (EU), the United Kingdom (UK), Norway, the Faroe Islands and Iceland. Two games are considered. First, a four-player game where the UK is still a member of the EU. Second, a five-player game where the UK is no longer a member of the union. Each game is modelled in two stages. In the first stage, players form coalitions following a predefined set of rules. In the second stage, given the coalition structure that has been formed, each coalition choose the economic strategy that maximises its own net present value of the fishery given the behaviour of the other coalitions. The game is solved using backward induction to obtain the set of Nash equilibria coalition structures in pure strategies, if any. We find out that the current management regime is among the stable coalition structures in all eight scenarios of the four-player game, but in only one case of the five-player game. In addition, stability in the five-player game is sensitive to the growth function applied and the magnitude of the stock elasticity parameter.

Coalitional Games for Downlink Multicell Beamforming

A coalitional game is proposed for multicell multi-user downlink beamforming. Each base station intends to minimize its transmission power while aiming to attain a set of target signal-to-interference-plus-noise-ratio (SINR) for its users. To reduce power consumption, base stations have incentive to cooperate with other base stations to mitigate intercell interference. The coalitional game is introduced where base stations are allowed to forge partial cooperation rather than full cooperation. The partition form coalitional game is formulated with the consideration that beamformer design of a coalition depends on the coalition structure outside the considered coalition. We first formulate the beamformer design for a given coalition structure in which base stations in a coalition greedily minimize the total weighted transmit power without considering interference leakage to users in other coalitions. This can be considered as a non-cooperative game with each player as a distinct coalition. By introducing cost for cooperation, the coalition formation game is considered for the power minimization-based beamforming. A merge-regret-based sequential coalition formation algorithm has been developed that is capable of reaching a unique stable coalition structure. Finally, an ${\alpha }$ -Modification algorithm has been proposed to improve the performance of the coalition formation algorithm.

A cooperative game with envy

This paper proposes an envy-incorporated cooperative game model and investigates the envy effects on players' coalition-forming and payoff-allocating decisions. A player's utility depends on her/his own payoff and the envy toward other players, inside and outside the same coalition, with higher payoffs. Envy core is defined to characterize stable coalition structures and payoff allocations of this new game. Conditions for the envy core to be nonempty are provided. The relative significance of in-coalition envy and out-coalition envy is shown to be a key factor to the form of the envy core. Application to a simple game shows that envy may significantly change players' decisions.

Resource Provisioning for Cloud-Assisted Software Defined Wireless Sensor Network

Due to the significant advancement of wireless and mobile technology, the applications targeted for these are getting more and more complex and demanding of high power and resources. The cloud-assisted software-defined wireless sensor networking (CSDWSN) paradigm has emerged as a promising solution to perform these highly demanding tasks with the help of powerful cloud servers. However, due to the dynamic variation in sensor users demands, it is becoming challenging for a single CSDWSN provider to always provide a sufficient amount of computing resources to fulfill users needs. This paper exhibits an approach of resource and revenue sharing with coalition development among CSDWSN providers. The proposed method models the collaborations among the CSDWSN providers as a coalition game. As opposed to existing methodologies, the game model goes for amplifying the individual revenue of CSDWSN providers with minimum energy consumption by analyzing their internal users demand and dynamic pricing strategy. In addition, the proposed game enables a socially optimal and stable coalition structure, which leads to both increased total profit of a federation and improved equality among participating CSDWSN providers. Various simulation experiments were completed to demonstrate the viability of the proposed cooperative game model.

Adaptive Pilot Clustering in Heterogeneous Massive MIMO Networks

We consider the uplink of a cellular massive MIMO network. Acquiring channel state information at the base stations (BSs) requires uplink pilot signaling. Since the number of orthogonal pilot sequences is limited by the channel coherence, pilot reuse across cells is necessary to achieve high spectral efficiency. However, finding efficient pilot reuse patterns is non-trivial especially in practical asymmetric BS deployments. We approach this problem using coalitional game theory. Each BS has a few unique pilots and can form coalitions with other BSs to gain access to more pilots. The BSs in a coalition thus benefit from serving more users in their cells, at the expense of higher pilot contamination and interference. Given that a cell's average spectral efficiency depends on the overall pilot reuse pattern, the suitable coalitional game model is in partition form. We develop a low-complexity distributed coalition formation based on individual stability. By incorporating a base station intercommunication budget constraint, we are able to control the overhead in message exchange between the base stations and ensure the algorithm's convergence to a solution of the game called individually stable coalition structure. Simulation results reveal fast algorithmic convergence and substantial performance gains over the baseline schemes with no pilot reuse, full pilot reuse, or random pilot reuse pattern.

United We Stand or Divided We Stand? Strategic Supplier Alliances Under Order Default Risk

We study the alliance formation strategy among suppliers in a framework with one downstream firm and n upstream suppliers. Each supplier faces an exogenous random shock that may result in an order default. Each of them also has access to a recourse fund that can mitigate this risk. The suppliers can share the fund resources within an alliance, but they need to equitably allocate the profits of the alliance among the partners. In this context, suppliers need to decide whether to join larger alliances that have better chances of order fulfillment or smaller ones that may grant them higher profit allocations. We first analytically characterize the exact coalition-proof Nash-stable coalition structures that would arise for symmetric complementary or substitutable suppliers. Our analysis reveals that it is the appeal of default risk mitigation, rather than competition reduction, that motivates cooperation. In general, a riskier and/or less fragmented supply base favors larger alliances, whereas substitutable suppliers and customer demands with lower pass-through rates result in smaller ones. We then characterize the stable coalition structures for an asymmetric supplier base. We establish that grand coalition is more stable when the supplier base is more homogeneous in terms of their risk levels, rather than divided among a few highly risky suppliers and other low-risk ones. Going one step further, our investigation of endogenous recourse fund levels for the suppliers demonstrates how financing costs affect suppliers’ investments in risk-reducing resources and, consequently, their coalition formation strategy. Last, we discuss model generalizations and show that, in general, our insights are quite robust. This paper was accepted by Serguei Netessine, operations management.

Evolutionary coalitional games for random access control

This paper considers a random access system with several users and one shared medium. Each user has its own queue (of packets) which can be empty or not. We propose an evolving coalitional game between the users and analyze the system outcomes. Unlike classical coalitional approaches that assume that coalitional structures are fixed and formed cost-free, we explain how coalitions can be formed in a fully distributed manner using evolutionary dynamics and coalitional combined fully distributed payoff and strategy (CODIPAS) learning. We introduce the concept of evolutionarily stable coalitional structure (ESCS), which, when it is formed, is resilient to small perturbation of strategies. We show that (1) the formation and the stability of coalitions depend mainly on the cost of making a coalition compared to the benefit of cooperation, (2) the grand coalition can be unstable and a localized coalitional structure is formed as an evolutionarily stable coalitional structure. When the core is empty, the coalitional CODIPAS scheme selects one element of the stable set. Finally, we discuss the convergence and complexity of the proposed coalitional learning in access control with different users’ activities. Some extensions to cognitive medium access control with queue management are provided.

Internal hierarchy and stable coalition structures

In deciding whether to join a coalition or not, an agent must consider both i) the expected power of the coalition and ii) her position in the vertical structure within the coalition. We establish the existence of a positive relationship between the degree of inequality in remuneration within coalitions and the number of coalitions to be formed endogenously in stable systems. We show that such coalitions can be mixed and balanced, rather than segregated, in terms of members' ability levels. In any stable system each coalition is of an efficient size and every agent is paid her marginal contribution.

Distributed Long-Term Base Station Clustering in Cellular Networks Using Coalition Formation

Interference alignment (IA) is a promising technique for interference mitigation in multicell networks due to its ability to completely cancel the intercell interference through linear precoding and receive filtering. In small networks, the amount of required channel state information (CSI) is modest and IA is, therefore, typically applied jointly over all base stations. In large networks, where the channel coherence time is short in comparison to the time needed to obtain the required CSI, base station clustering must be applied however. We model such clustered multicell networks as a set of coalitions, where CSI acquisition and IA precoding are performed independently within each coalition. We develop a long-term throughput model, which includes both CSI acquisition overhead and the level of interference mitigation ability as a function of the coalition structure. Given the throughput model, we formulate a coalitional game where the involved base stations are the rational players. Allowing for individual deviations by the players, we formulate a distributed coalition formation algorithm with low complexity and low communication overhead that leads to an individually stable coalition structure. The dynamic clustering is performed using only long-term CSI, but we also provide a robust short-term precoding algorithm, which accounts for the intercoalition interference when spectrum sharing is applied between coalitions. Numerical simulations show that the distributed coalition formation is generally able to reach long-term sum throughputs within 10% of the global optimum.

Stochastic Approach for Determining Stable Coalition Structure

In this paper, we study TU-games with coalition structure and propose an approach for determining a stable coalition structure solving a stochastic game of a special form. Using a Nash equilibrium in this game, we draw an analogy between the stable coalition structure and an absorbing state in a Markov chain. In addition, we consider a case of restricted coalitions assuming that not all coalitions are feasible and extend the definition of the stable coalition structure to this case.

Overlapping coalition formation games‐based resource allocation for device‐to‐device communication in LTE‐A network

AbstractIn the long‐term evolution‐advanced system, device‐to‐device (D2D) communication brings many significant benefits, such as low power consumption, low delay, high bit rates and efficient frequency utilisation. However, these potential advantages hinge on the intelligent resource allocation approach between D2D user equipments (DUEs) and cellular user equipments (CUEs). Different from existing work that focused on the scenario that one CUE shares spectrums with one D2D pair and thus disjoint groups are formed to use spectrums, in our paper, we proposed a coalition formulation game with overlapping coalitions. In this game, we model the resource sharing problem as a transferable coalition formation game where there exists intersection among these coalitions and the DUEs can make a decision to join or leave a coalition according to the merge‐and‐split rule. Consequently, not only one D2D pair can employ the same resource with multiple CUEs but also the channel of one CUE can be allocated to multiple D2D pairs in order to maximise the frequency efficiency and the system sum throughput. In particular, we consider the practical case and study the effect that only imperfect channel state information (CSI) can be obtained on the stable coalition formation game. A discrete‐time Markov chain‐based analysis is presented to obtain the stable coalition structure, and the complexity of employing this scheme is evaluated. Extensive numerical results show that the proposed overlapping coalition formulation game‐based scheme results in better performance compared to the traditional existing methods even in the imperfect CSI scenarios. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian Coalitional Game in Physical Layer Security

Cooperative communication has been recently investigated as an attractive way to improve the physical layer security of wireless network. However, in practical situation, the node's behavior in the coalition is either cooperative or not due to the environment the mobile node located. Wireless network nodes do not have an exact and perfect knowledge of the cooperative behavior of the potential cooperators in coalition formation. In order to form the stable coalitional structure under behavior uncertainty of nodes, we propose the Bayesian Coalitional Games using partition model based on possible worlds (i.e. environments), which nodes enter into contracts (i.e. agreements) with one another to deal with the uncertain payoffs. We obtain the Bayesian core which is the Nash-stable and fair coalitional structure. A belief update mechanism to the nodes with cooperative behavior uncertainty is used to calculate the probability of each possible world. We also present a discrete-time Markov chain model to investigate the stability of the coalitional structure. Preliminary experimental evidence demonstrates the effectiveness of our approach.

Analysis of retailers’ coalition stability for supply chain based on LCS and stable set

To attain the general form of stable coalition structure, this paper addressed the problem of retailers’ coalition stability in a two-stage supply chain consisting of one supplier and multiple retailers. A profit gain function was established via introducing market gain coefficient and coalition cost coefficient for different coalition structures. Based on the function, the profit of each retailer in all kinds of coalition structures was analysed, and the general feature of a stable coalition structure was attained by the largest consistent set method and the stable set method. Furthermore, some insights were obtained. For example, stable coalition structures are equidistributed or approximate equidistributed; with supplier’s cost increasing, the size of the retailers’ coalition increases. Finally, the above conclusions are verified by numerical simulation. The results of this paper provide a reference for retailers’ coalition in a supply chain, such as automobile or Information Technology supply chain.

Toward the complexity of the existence of wonderfully stable partitions and strictly core stable coalition structures in enemy-oriented hedonic games

We study the computational complexity of the existence and the verification problem for wonderfully stable partitions (WSPE and WSPV) and of the existence problem for strictly core stable coalition structures (SCSCS) in enemy-oriented hedonic games. In this note, we show that WSPV is NP-complete and both WSPE and SCSCS are DP-hard, where DP is the second level of the boolean hierarchy, and we discuss an approach for classifying the latter two problems in terms of their complexity.

Rate Allocation Based on Coalition Formation Game in Low Power Collaborative Transmission

To realize collaborative transmission in wireless overlay access networks, the question of rate allocation arises as how to divide the traffic flow among heterogeneous networks. Different networks role as game players and they try to transmit the traffic flow by a cooperative method. Power costs and transmission capabilities in heterogeneous networks are different according to terminal position, network load etc, so the grand coalition is not always beneficial and the coalition structure should be adjusted in time. With the power cost introduced in the utility function, the rate allocation is formulated in a coalition formation game framework in the paper. The stable coalition structure is formed with the merge-and-split rule, then the utility is distributed to different players and the transmission rates in different networks are determined. Such a process continues until the end of the traffic transmission. The theoretical and experimental results are presented to validate our proposed method. Compared with the Nash Bargaining Solution and the Shapley value, the coalition structure can be adjusted with the terminal position through the new scheme and then the highest coalition utility can be obtained with low power cost. Moreover, the proposed method turns to be the bargaining game framework if the power cost is not considered.

Energy-Efficient Topology Control With Selective Diversity in Cooperative Wireless Ad Hoc Networks: A Game-Theoretic Approach

Due to the scarce bandwidth and limited power supply in mobile terminals, performance and energy consumption in wireless communications must be continually focused upon. Cooperative transmissions improve the capacity performance of wireless ad hoc networks (WANETs). However, when energy efficiency is considered, the advantage of user cooperation over non-cooperation does not always exist since it involves multiple nodes with more energy consumption in transmissions. To exploit the benefits of user cooperation in cooperative WANETs, we propose a distributed energy-efficient selective diversity (EESD) topology control to improve energy efficiency, which jointly considers network capacity and energy consumption in terms of bits per Joule . EESD forms transmission coalitions via cooperative manner (i.e, diversity) selection, by taking into account the cost of channel information exchange. We then formulate EESD as a coalition game and propose an adaptive coalition formation algorithm for EESD with proved convergence property and stable coalition structures. Simulation results show the performance improvement of EESD in energy efficiency and network lifetime compared to the existing topology control schemes.

A dynamic coalition formation framework for interference management in dense small‐cell networks

AbstractIn response to the drastic increase in the traffic loads being served by existing cellular wireless networks, small cells are envisioned as a promising solution to extend the coverage and offload the traffic from the overburdened macrocells. However, the interference management amongst densely deployed small cells remains a technical challenge. In this paper, a neighbourhood cooperation‐based interference mitigation scheme is proposed. By forming coalitions, the transmissions of small‐cell base stations (SBSs) within the coalition are coordinated, and the co‐tier interference amongst them is thus suppressed. Considering the facts that SBSs are selfish and rational, the cooperative behaviour of the neighbourhood SBSs is formulated as a coalition game in partition form. To achieve a final stable coalition structure, the concept of recursive core is first introduced. Then a simple distributed merge‐only algorithm is proposed, and its performance, in terms of stability, convergence and complexity, is theoretically analysed. The dynamic process of the coalition formation is further investigated. Simulation results show that the proposed algorithm can improve the individual throughput of SBS by 5.6% and 27.3%, respectively, when compared with the classical and non‐cooperative cases. Copyright © 2014 John Wiley & Sons, Ltd.

New coalition formation game for spectrum sharing in cognitive radio networks

SUMMARYIn cognitive radio networks, Secondary Users (SUs) can access the spectrum simultaneously with the Primary Users (PUs) in underlay mode. In this case, interference caused to the licensed users has to be effectively controlled. The SUs have to make spectrum access decisions in order to enhance their quality of service, but without causing harmful interference to the coexisting PUs. In this paper, we propose a cooperative spectrum decision, which enables the SUs to share the spectrum with the PUs more efficiently. Our approach is based on a new coalitional game in which the coalition value is a function of the SUs' spectral efficiencies, the inter‐SUs interference, and the interference caused to the PUs. By applying new Enter and Leave rules, we obtain a stable coalition structure. Simulation results show that the SUs' spectral efficiencies are considerably increased and that the interference caused to the coexisting PU is reduced by about 7.5% as compared to an opportunistic spectrum access scheme. Moreover, the proposed coalitional game results in a more balanced spectrum sharing in the network. Copyright © 2014 John Wiley & Sons, Ltd.