Coalition Structure Research Articles

Can partial cooperation between developed and developing countries be stable?

We consider an asymmetric differential game of pollution control with a developing country and two developed countries. The developing country is invulnerable to the pollution in contrast to the developed ones. Assuming partial cooperation, we examine all coalition structures composed by three players and provide the stability conditions for them using two approaches: (i) Nash stability, (ii) individual stability. First, the case of nontransferable payoffs is examined. Second, a transfer payment scheme is proposed to make particular coalition structures stable.

Coalition formation problems with externalities

We study coalition formation problems with externalities. We prove that, if expectations are not prudent a stable coalitions structure may fail to exist. Under prudent expectations a stable and efficient coalition structure exists if the set of admissible coalitions is single-lapping. However, under this assumption the stable set is not a singleton, and no stable strategy-proof revelation mechanism exists, differently from the case without externalities. Finally, the stable correspondence is Nash implementable.

Reaching Individually Stable Coalition Structures

The formal study of coalition formation in multi-agent systems is typically realized in the framework of hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this article, we study the convergence of simple dynamics leading to stable partitions in a variety of established classes of hedonic games, including anonymous, dichotomous, fractional, and hedonic diversity games. The dynamics we consider is based on individual stability: an agent will join another coalition if she is better off and no member of the welcoming coalition is worse off. Our results are threefold. First, we identify conditions for the (fast) convergence of our dynamics. To this end, we develop new techniques based on the simultaneous usage of multiple intertwined potential functions and establish a reduction uncovering a close relationship between anonymous hedonic games and hedonic diversity games. Second, we provide elaborate counterexamples determining tight boundaries for the existence of individually stable partitions. Third, we study the computational complexity of problems related to the coalition formation dynamics. In particular, we settle open problems suggested by Bogomolnaia and Jackson, Brandl et al., and Boehmer and Elkind.

Generalization of the social coalitional equilibrium structure

We generalize the notion of Ichiishi (Econometrica 49(2):369–377, 1981)’s social coalitional equilibrium to a multi-layered coalition structure with parameters, in which agents can incorporate simultaneously multiple coalition structures with multiple independent coalition-deviation opportunities. For each opportunity, agents play a social coalitional equilibrium (SCE) game, called a sub-parametric SCE game, constrained by external environment (parameters and joint decisions of all other sub-parametric SCE games). The generalized social coalitional equilibrium (GSCE) concept is, therefore, considered to be a synthesis of the Nash equilibrium concept and the cooperative solution concept. We provide the definition of GSCE and give the proof of existence theorem. Through some applications to general equilibrium models, the GSCE concept provides a conceptual framework for describing coexisting different industries having independent investment opportunities and their simultaneously determined industrial organizations.

Coalition Structure Generation in Edge Computing Environment With Multitasking Concurrency

Edge computing (EC) is a distributed computing paradigm that brings computation and data storage closer to the data sources. With the rapid development of EC, offloading scientific computing and data processing tasks from end devices to edge nodes (ENs) can satisfy these tasks’ requirements. However, a single EN with limited computing capacity is usually insufficient to handle these tasks. Hence, using a coalition structure (CS) of many ENs to handle multiple concurrent tasks in an EC environment becomes a feasible scheme. Still, many existing methods cannot be used directly in this scenario because of enormous CS solution space, low search speed, long-running time, poor optimal solution quality, etc. In response, we propose an arbitrary discrete political optimizer (ADPO) algorithm with a discrete recent-past position updating strategy to explore the potential CS space. Unlike other heuristic algorithms, ADPO further improves the better solutions by interacting with each other in the parliamentary affairs phase. After that, we formulate an integer programming (IP) optimization model to alleviate the low search speed or long time consuming. Finally, extensive experiments demonstrate that ADPO is superior to the existing heuristic algorithm. In addition, the IP model excels in exiting algorithms at the running time (milliseconds level) and resource occupied ratio.

Stakeholder discourse coalitions and polarisation in the hen harrier conservation debate in news media

Abstract Conservation conflicts are complex and can be deep‐rooted, with stakeholders holding entrenched policy positions. The actors involved producing verbal interconnected interactions that form policy debates. Thus, conservation debates can be viewed as network phenomena with stakeholders forming coalitions in support of, or opposition to, certain policies and practices. We used Discourse Network Analysis of print media to investigate the structure and dynamics of the stakeholder debate around the management of hen harriers Circus cyaneus, a bird of prey at the centre of a long‐standing conservation conflict in the United Kingdom. We aimed to determine whether the structure of discourse coalitions changed among the diverse aspects of the debate and whether the polarisation of the debate has changed through time. Our search and selection criteria led to the analysis of 737 statements within 131 newspaper articles published from August 1993 to December 2019. We show that, while the discourse network of the overall debate is quite unstructured, actors formed divergent coalitions when defining the conservation problem and its solutions. In contrast, discourses converged around reactions with positive or negative emotions in relation to events and issues of hen harrier conservation. Polarisation among actors has increased over time and peaked in the second half of the 2010s, concurrent with the release of the species recovery plan. Our study highlights the value of analysing discourse networks in conservation policy debates. Discourse networks reveal which aspects of any conservation problem cause stakeholders to converge or diverge and can identify periods of intensified debate that, ultimately, contribute to informing conflict mitigation and resolution processes. Read the free Plain Language Summary for this article on the Journal blog.

Blockholdings in closely held corporations: An analysis of ownership coalitions in emerging countries

Blockholdings in closely held corporations have been examined in the literature to understand the importance of the size and structure of minimal coalitions in a volatile macroeconomic environment. We show, theoretically and empirically, that three-member minimal controlling coalitions provide the best performance results because the portfolio of potential strategies of such coalitions can increase strategic choices in the boom-bust-recovery cycle, but coordination costs are not that high. We also show that “competition” between potential minimal controlling coalitions (of the same firm) with two or more members improves the firm’s performance. With respect to the characteristics of the institutional owners of one-member controlling coalitions, we found that firms controlled by foreigners and/or other non-financial firms and financial holdings performed better than the average firm. Our study indicates that the change of ownership structures in emerging countries is determined by the extant economic systems and through administrative interventions.

Quasi-Owen Value for Games on Augmenting Systems with a Coalition Structure

This paper focuses on games on augmenting systems with a coalition structure that can be seen as an extension of games with a coalition structure and games on augmenting systems. Considering the player payoffs, the quasi-Owen value is defined. To show the rationality of this payoff index, five representative axiomatic systems are established. The population monotonic allocation scheme (PMAS) and the core are introduced. Moreover, the relationships between the PMAS and quasi-Owen value as well as the core and quasi-Owen value are discussed. Finally, an illustrative example is given to show the concrete application of the new payoff indices.

Selective Exploration Algorithm for Coalition Formation

Coalition formation with task dependencies has been the focus of few of the literature on multi-agent coalition formation. In contrast, very little attention has been given to the case where each agent has several alternative sets of tasks leading it to its goal satisfaction. The task dependencies impact the feasibility of the coalitions depending on the considered tasks alternative at a given time. Hence, the performance of a single task, whether by coalition formation (group of agents) or by a single performance, could affect the feasibility of other coalitions in the system. However, these task dependencies play a crucial role in many real-world multi-agent applications. Against this background, we consider in this paper multiple self-interested agents each of which has a goal it needs to achieve by performing a set of tasks. Each agent has several alternative sets of tasks leading it to its goal satisfaction. The tasks in an alternative exhibit dependencies and require sequential execution. So, to jointly achieve goals, the agents may form interdependent coalitions. We introduce a new algorithm that we call the Selective Exploration Algorithm (SEA) for coalition formation that accounts for the task dependencies to consider only feasible coalitions and reduce the size of the search space to explore and identify the optimal coalition structure.

Coordination of two competing closed-loop supply chains: A cooperative game approach

In the development of end-of-life (EOL) products recycling, coordinating competing closed-loop supply chains (CLSCs) with restricted coalition has become an important topic that has yet to be thoroughly investigated. In this study, we first investigate the possible coalitions for two CLSCs composed of manufacturers and third-party recyclers under a restricted coalition structure, which is used for deriving the characteristic functions representing the bargaining powers of different coalitions and allocating the overall profits. Subsequently, to fairly allocate the maximal profit, we establish a cooperative game in the form of characteristic function for the two CLSCs and use an advanced solution concept (average tree value) to coordinate them. We find that: compared to other non-cooperative and partial cooperative models, the centralized model can always achieve the best performance, e.g., the highest recovery rate. And the profit of the fully centralized model increases linearly with the increase of the cooperation coefficient. When the third-party recyclers of two CLSCs form alliance, the profit of the manufacturer is positively or negatively correlated with the cooperation coefficient due to the difference of the model and price elasticity coefficient. Under the cooperation of two CLSCs third-party recyclers, the relationship between the profit of the third-party recycler, the profit of the single chain system or the profit of the double chain system and the cooperation coefficient increases first and then decreases, but the inflection point is different. The coordination of two competing CLSCs can be well addressed by the allocation scheme proposed in this study, while satisfying the collective and individual rationalities.

Connectivity Guarantee Within UAV Cluster: A Graph Coalition Formation Game Approach

Unmanned Aerial Vehicle (UAV) clustering is promising for performing large-scale missions because of high mobility and easy deployment. However, the connectivity problems caused by the high mobility of UAVs and the interferences are mostly ignored in existing UAV mission executions. Rapid restoration of UAV network connectivity is essential for preventing communication disruption and improving the overall network performance. Thus, a graph coalition formation game that integrates the UAV time-varying topology graph with the coalition formation game is proposed to rapidly restore the connectivity of the UAV network in need. The method improves the utility of UAV clustering and ensures the network connectivity. Then, a graph coalition formation game algorithm based on the shortest path tree (SPT-GCF) rapidly forms an approximately optimal coalition structure. The simulation results show that the proposed approach increases the average utility of UAV clustering by 6.5% and 14.5% respectively when compared with the existing non-overlapping coalition formation game (NOCFG) and the coalition formation game without considering the cluster connectivity.

INTERNAL STABILITY AND PARETO OPTIMALITY IN HEDONIC COALITION FORMATION GAMES

We study hedonic coalition formation games that consist of a finite set of agents and a list of agents’ preferences such that each agent’s preferences depend only on the members of her coalition. An outcome of a hedonic coalition formation game is a partition (i.e., coalition structure) of the finite set of agents. We study the existence of partitions that are both internally stable and Pareto optimal. We construct an algorithm that terminates for each given hedonic coalition formation game such that the outcome of the algorithm is internally stable and Pareto optimal. We also show that if the outcome of the algorithm is the partition that consists of singleton coalitions then it is also core stable and if it is the partition that contains only the grand coalition then it is also both core stable and Nash stable.

Union-wise egalitarian solutions in cooperative games with a coalition structure

Union-wise egalitarian solutions in cooperative games with a coalition structure

Approximately Socially-Optimal Decentralized Coalition Formation with Application to P2P Energy Sharing

The paradigm of P2P (peer-to-peer) economy has emerged in diverse areas. P2P energy sharing is a new form of P2P economy in the energy sector, which allows users to establish longer-term sharing arrangements of their local energy resources (e.g., rooftop PVs, home batteries) with joint optimized energy management. In such a P2P setting, a coalition of users is formed for sharing resources in a decentralized manner by self-interested users based on their individual preferences. A likely outcome of decentralized coalition formation will be a stable coalition structure, where no group of users could cooperatively opt out to form another coalition that induces higher preferences to all its members. Remarkably, there exist a number of fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games) that model practical cost-sharing applications with desirable properties, such as the existence of a stable coalition structure with a small strong price-of-anarchy (SPoA) to approximate the social optimum. In this paper, we provide general results of decentralized coalition formation: (1) We establish a logarithmic lower bound on SPoA, and hence, show several previously known fair cost-sharing mechanisms are the best practical mechanisms with minimal SPoA. (2) We show that the SPoA of egalitarian and Nash bargaining cost-sharing mechanisms to match the lower bound. (3) We derive the SPoA of a mix of different cost-sharing mechanisms. (4) We present a decentralized algorithm to form a stable coalition structure. (5) Finally, we apply our general results to P2P energy sharing and present an empirical study of decentralized coalition formation in a real-world project. We study the empirical SPoA, which is observed within 95% of the social optimal cost with coalitions of 2 and 3 users, via fair cost-sharing mechanisms.

Strong Players and Stable Coalition Structures in PMAS Profit Game

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions.

Two-step Shapley-solidarity value for cooperative games with coalition structure

This paper proposes an alternative for the two-step Shapley value for cooperative games with coalition structure that has earlier been proposed by Kamijo. The value is based on the idea that within a union of players, worth should be distributed based on the solidarity principle. Specifically, we propose a two-step Shapley-solidarity value, in which the surplus of a union’s Shapley value in the quotient game is distributed equally among the union’s members, and players obtain the solidarity value of the respective subgame within their union. We provide an intuitive procedural characterization for this value and give three axiomatizations to pinpoint the differences to comparable values.

Layered Networks, Equilibrium Dynamics, and Stable Coalitions

An important aspect of network dynamics that has been missing from our understanding of network dynamics in various applied settings is the influence of strategic behavior in determining equilibrium network dynamics. Our main objective hear to say what we can regarding the emergence of stable club networks—and therefore, stable coalition structures—based on the stability properties of strategically determined equilibrium network formation dynamics. Because club networks are layered networks, our work here can be thought of as a first work on the strategic dynamics of layered networks. In addition to constructing a discounted stochastic game model (i.e., a DSG model) of club network formation, (1) we show that our DSG of network formation possesses a stationary Markov perfect equilibrium in players’ membership-action strategies; (2) we identify the assumptions on primitives which ensure that the induced equilibrium Markov process of layered club network formation satisfies the Tweedie Stability Conditions (Tweedie in Stoch Process Appl 92:345–354, 2001) and (3) we show that, as a consequence, the equilibrium Markov network formation process generates a unique decomposition of the set of state-network pairs into a transient set together with finitely many basins of attraction. Moreover, we show that if there is a basin containing a vio set (a visited infinitely often set) of club networks sufficiently close together, then the coalition structures across club networks in the vio set will be the same (i.e., closeness across networks in a vio set leads to invariance in coalition structure across networks in a vio set).

Vein-Based Coalitions for Multi-Agent Pattern Formation Tasks

This letter explores the vein trait of the structural formation task and extracts four typical parallel-straight vein structures for generating coalitions. Then, the Vein-Based Multi-Agent Pattern Formation (VB-MAPF) method is proposed to resolve task and path planning on coalitions. Besides, the presented rectifying operation guarantees the optimal coalition structure, and the vein-based pruned conflict-based search reduces the searching space for collision-free path planning. Compared with typical solvers, the inter-performance and the intra-performance orders show the efficiency and scalability of the VB-MAPF method in terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">makespan</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">average distance</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">maximum distance</i> on dozens of coalitions and thousands of agents.

Tracing coalition changes in knowledge in and engagement with childhood obesity prevention to improve intervention implementation

BackgroundWhile most coalition research focuses on studying the effects of peer relationship structure, this study examines the coevolution of coalition structure and behavior across three communities in the U.S. with the goal of identifying coalition dynamics that impact a childhood obesity prevention intervention. MethodsOver two years (2018–2020), three communities within the U.S. participated in a childhood obesity prevention intervention at different times. This intervention was guided by the Stakeholder-Driven Community Diffusion theory, which describes an empirically testable mechanism for promoting community change. Measures are part of the Stakeholder-driven Community Diffusion (SDCD) survey with demonstrated reliability, which include knowledge of and engagement with childhood obesity prevention and social networks. Data from three coalition-committees and their respective networks were used to build three different stochastic actor-oriented models. These models were used to examine the coevolution of coalition structure with coalition behavior (defined a priori as knowledge of and engagement with obesity prevention) among coalition-committee members and their nominated alters (Network A) and coalition-committee members only (Network B). ResultsOverall, coalitions decrease in size and their structure becomes less dense over time. Both Network A and B show a consistent preference to form and sustain ties with those who have more ties. In Network B, there was a trend for those who have higher knowledge scores to increase their number of ties over time. The same trend appeared in Network A but varied based on their peers’ knowledge in and engagement with childhood obesity prevention. Across models, engagement with childhood obesity prevention research was not a significant driver of changes in either coalition network structure or knowledge.ConclusionsThe trends in coalition Network A and B’s coevolution models may point to context-specific features (e.g., ties among stakeholders) that can be leveraged for better intervention implementation. To that end, examining tie density, average path length, network diameter, and the dynamics of each behavior outcome (i.e., knowledge in and engagement with childhood obesity prevention) may help tailor whole-of-community interventions. Future research should attend to additional behavioral variables (e.g., group efficacy) that can capture other aspects of coalition development and that influence implementation, and to testing the efficacy of network interventions after trends have been identified.

Second-order productivity, second-order payoffs, and the Owen value

We introduce the concepts of the components’ second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components’ second-order payoffs for one-point solutions for CS games as generalizations of the players’ second-order productivities in TU games and of the players’ second-order payoffs for one-point solutions for TU games (Casajus in Discrete Appl Math 304:212–219, 2021). The players’ second-order productivities are conceptualized as second-order marginal contributions, that is, how one player affects another player’s marginal contributions to coalitions containing neither of them by entering these coalitions. The players’ second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components’ second-order productivities are conceptualized as their second-order productivities in the game between components; the components’ second-order payoffs are conceptualized as their second-order payoffs in the game between components. We show that the Owen value is the unique efficient one-point solution for CS games that reflects the players’ and the components’ second-order productivities in terms of their second-order payoffs.