Stable Coalition Research Articles

Stability for Coalition Structures in Terms of the Proportional Partitional Shapley Value

AbstractMany coalitional values have been introduced in the literature on cooperative games over the last decades, and especially since 2000. The multiplicity of options suggests the convenience of testing the existence of stable coalition structures, in the sense of Hart and Kurz (1983, Econometrica), when payments are made using some of these values. We recall their concept of $$\gamma$$ γ –stability and give results for the proportional partitional Shapley value, introduced by Alonso–Meijide et al (2015, Discrete Appl. Math.), which shares the utility of any coalition proportionally to the Shapley value of the involved players in the original game.

Interrelationships of Non-cooperative, Classical and Pareto coalitional stability definitions

Theorems are established on the interrelationships among non-cooperative, classical and Pareto coalitional stability definitions within the framework of the graph model for conflict resolution. The classical coalition stability concepts are first redefined and then, based on the concept of Pareto coalition improvement, new definitions are proposed for Pareto coalition Nash, Pareto coalition general metarational, Pareto coalition symmetric metarational, and Pareto coalition sequential stability. Relations among Pareto coalition stability definitions, earlier coalition stability definitions, and non-cooperative analogues are explained. The practical applicability of these stability definitions is illustrated through their application to a real-world conflict, a 2014 offshore oil exploration dispute in the South China Sea. The equilibrium results confirm the theoretical validity of the new definitions, and show that valuable insights that can be garnered using the Pareto coalition stability approach.

Incentivizing energy and carbon rights transactions among network-constrained energy hubs: Cooperative game with externalities

Joint energy and carbon rights transactions for multiple energy hubs could boost the utilization of renewable distributed energy resources and reduce carbon emissions in energy sectors. The joint transaction mechanism based on the cooperative game is proposed, in which cooperative energy hubs form a grand coalition to share diverse forms of energy and carbon rights in order to maximize their total benefit. Furthermore, the grand coalition-based transaction mechanism is augmented with network constraints to account for the influence of network constraints on the trading behaviors of energy hubs, which is mathematically represented as a cooperative game with externalities. In addition, mathematical proof is provided to demonstrate the stability of the formed network-constrained grand coalition. To determine the trading behaviors and allocate payoff among energy hubs while satisfying both network constraints and coalition stability, a scalable two-stage optimization structure is provided, with the first stage ensuring coalition stability and the second preventing network constraint violations. A solution technique combined with Karush-Kuhn-Tucker conditions and Benders decomposition is proposed to solve the two-stage optimization problem. The effectiveness and scalability of the proposed joint transaction mechanism and the solution technique are supported by numerical results for the 4-EH and 33-EH systems. The introduction of the carbon market leads to a 20.6 % reduction in carbon emissions and a 10.5 % increase in total payoff by facilitating peer-to-peer trading of both energy and carbon rights.

Altruistic behavior and international environmental agreements: a differential game approach

AbstractIn the last three decades International Environmental Agreements (IEAs) have been widely analyzed. Classic models predict that only coalitions formed by a few countries can be stable, generating a rich literature devoted to solving the small coalition puzzle. The fundamental idea behind the great part of the literature is that players are selfish: to achieve a large stable coalition it is necessary to design an agreement that includes a credible system of incentives or punishments. The aim of this model is to study the effects, on equilibrium strategies and on the stability of an IEA, of players that do not look only at their own interests, but that take care of the wellness of the other players in coalition. Following the approach of the Paris Agreement in 2015, countries that join the coalition do not decide emissions collectively, but each of them sets their own emissions. The model is the usual two-step game: first the players have to choose whether they want to join the coalition or not, in the second step they solve a Nash differential game to find the optimal emissions. The stability of the coalition is studied in two cases: (i) with the classic internal and external stability, (ii) defining an altruistic stability condition.

Partial Server Pooling in Delay Systems

We consider a strategic resource pooling interaction between two service providers, each of which is modelled as a multi-server queue. The traditional full resource pooling mechanism, while improving the overall system performance measure, may not always benefit the providers individually. For rational service providers, there will therefore be no incentive to form a stable coalition. We address this issue by proposing three partial sharing mechanisms: two of these, Partial Pooling with Dedicated Servers and Partial Pooling with Repacking, allow each provider to designate a certain number of servers to potentially serve jobs of the other provider, while the third mechanism, Differential Queue Length, maintains an upper bound on the difference between occupancies of the two queues. We determine the probability of waiting for each of the three mechanisms and show through several numerical examples that their Pareto frontiers are non-empty. In particular, this shows that the proposed partial pooling mechanisms are individually beneficial to both providers and incentivize coalition formation in all situations. Finally, we apply bargaining theory to determine the operating point on the Pareto frontier.

Coalitional Pareto optimal solution of one differential game

This paper is devoted to the differential positional coalitional games with non-transferable payoffs (games without side payments). We believe that the researches of the objection and counter-objection equilibrium for non-cooperative differential games that have been carried out over the last years allow to cover some aspects of non-transferable payoff coalitional games. In this paper we consider the issues of the internal and external stability of coalitions in the class of positional differential games. For a differential positional linear-quadratic six-player game with a two-coalitional structure, the coefficient constraints are obtained which provide an internal and external stability of the coalitional structure.

Stability in Online Coalition Formation

Coalition formation is concerned with the question of how to partition a set of agents into disjoint coalitions according to their preferences. Deviating from most of the previous work, we consider an online variant of the problem, where agents arrive in sequence and whenever an agent arrives, they have to be assigned to a coalition immediately and irrevocably. The scarce existing literature on online coalition formation has focused on the objective of maximizing social welfare, a demanding requirement, even in the offline setting. Instead, we seek to achieve stable coalition structures in an online setting, and focus on stability concepts based on deviations by single agents. We present a comprehensive picture in additively separable hedonic games, leading to dichotomies, where positive results are obtained by deterministic algorithms and negative results even hold for randomized algorithms.

Coalition Stability in International Environmental Matching Agreements

This study presents empirically calibrated simulations of three different variants of environmental matching agreements aimed at reducing global greenhouse gas emissions. We determine whether matching agreements can produce larger stable coalitions and increase abatement contributions and payoffs as compared to standard agreements. The matching agreements we analyze feature uniform matching rates by which coalition members match the unconditional contributions of (i) the other coalition members, (ii) all other players, or (iii) only non-members, while non-members do not commit to any matching and maximize their individual payoffs. The simulation considers twelve asymmetric world regions with linear abatement benefits and quadratic costs, calibrated based on the STACO 3 model, and uses emissions data from the shared socioeconomic pathways database. We find that the first variant of the matching game fails to produce any stable coalitions and thus performs worse than the standard agreement that produces a stable two-player coalition. The second variant produces a stable grand coalition and significantly increases the abatement and payoff levels beyond the non-cooperative Nash baseline. Partial coalitions are unstable in this game. The third variant produces a two-player coalition similar to the standard coalition formation game, but with different members and higher abatement and payoff levels due to the matching mechanism.

International environmental agreements when countries behave morally

In the game-theoretical literature on forming international environmental agreements (IEAs) countries use to be self-interested materialists and stable coalitions are small. This paper analyzes IEA games with identical countries that exhibit Kantian moral behavior. Kantians are concerned with doing the right thing which means that they take those actions and only those actions that they advocate all others take as well. Countries may behave morally with respect to both emissions (reduction) and membership in an IEA. If countries are emissions Kantians or membership Kantians the equilibrium of the IEA games is socially optimal. To model more realistic Kantian behavior, we define an emissions [membership] moralist as a country whose welfare is a weighted average of the welfare of an emissions [membership] Kantian and a materialist. The game with emissions moralists produces stable coalitions not larger than those in the standard game with materialists. The game with membership moralists yields stable coalitions that are increasing in the membership morality. The aggregate emissions decline if the degree of morality of either type of moralists increases. Finally, we characterize the equilibrium of an IEA game with moderate moralists with respect to both emissions and membership.

Cooperation in spare parts systems with penalty cost per unit backlogged

Inventory pooling is well known to reduce inventory costs and improve customer service. Although potential benefits are well understood, one important prerequisite to form a stable coalition between independent companies, who like to cooperate to benefit from inventory pooling, is agreeing on a cost allocation such that no group of companies would better off leaving the coalition. Existence of such stable allocations would depend on the scenarios that these companies are cooperating in.In this paper, we study cooperation between a group of companies, who keep spare parts to maintain their expensive equipment, by pooling their inventory in several practically motivated scenarios. To address the cost allocation problem, we borrow concepts from cooperative game theory and examine the core of the resulting cooperative games in each scenario. We especially focus on systems with high penalty cost per unit backlogged, which is modelled as a well known (S−1,S) inventory system with backlogging.We study cooperation under four scenarios, namely cooperation under penalty cost, cooperation with joint capacity investment, cooperation under service level constraints and cooperation by inventory pooling. The first three scenarios consider cooperation by investing into a central pool of inventory optimally, whereas in the last scenario, companies cooperate by pooling their available inventory only. In most of the scenarios, we show the existence of stable cost allocations by identifying a core allocation, which is easy to compute and, in some, a population monotonic allocation (PMAS). In other scenarios, we present examples explaining why finding a stable allocation might not be possible by showing the core of the resulting games can be empty. To establish these results, we also derive several interesting properties (e.g. subhomogeneity of degree one) of the main performance measure (i.e., average number of backorders).

The strategic role of adaptation in international environmental agreements

This paper investigates the impact of the timing of adaptation on the stability of international environmental agreements (IEAs) for different levels of cooperation. This issue is addressed by solving a three-stage coalition formation game in a Nash-Cournot setting. In the first stage, countries decide non-cooperatively on their participation in an IEA. Then, depending on the timing, countries decide on adaptation and emissions in the second and third stage. The game is solved for three levels of cooperation. Countries can either cooperate on emissions (emission agreement), on adaptation (adaptation agreement), or both actions (complete agreement). When emissions are chosen first, this extension to an emission–adaptation game is a generalization of the pure emission game. However, when adaptation is chosen first, the grand coalition is stable, provided that countries sign a complete agreement. With partial cooperation, stable coalitions are small. The results establish a connection between the strategic role of adaptation, the levels of adaptation of non-signatories and signatories for the different types of agreements and the participation in an IEA. Moreover, the results indicate that the grand coalition is stable even when it significantly enhances net benefits.

Towards a more stable Construction Joint Venture agreement: individual rationality vs. fairness

Contractors’ decisions are individually rational and not always based on fairness that is needed in collaborative projects, such as Construction Joint Ventures (CJVs). This paper provides a comparative analysis between rational and fair-based sharing in CJVs risk management, along with the commonly used investment-based approach. The analysis is divided into two processes; (1) the contingency cost (CC) calculation process to generate the CCs based on the probabilities and impacts of the project’s different risk factors; and (2) the sharing process to allocate the payoff shares to the participating players using three different cooperative game theory (CGT) solution concepts, namely Kernel, Shapley value and τ-value. The analysis is carried out using two illustrative case studies drawn from the literature. The authors mathematically analyzed the stability of the coalition, and evaluated the results through a questionnaire survey held by construction practitioners to offer their perception on the proposed shares. The results show that fair-based approaches resulted in the most stable coalition formation compared to rational-based and investment-based shares. This shows the need to adopt fairness into the decision-making process of contractors in CJVs. Ultimately, this research shall help the decision-makers to craft agreements that stabilize collaborative construction projects.

A new integrated cooperative game and optimization model for the allocation of forest resources

We propose an integrated approach combining a cooperative game model and a multi-objective optimization model to determine the quantities of forest resources to allocate to several mills. The new mechanism developed in this study is applied to a regional case study in the province of Quebec (Canada), where public-owned forest resources should be allocated by the government to multiple competing mills. Collaboration between mills is considered in the upstream supply chain (i.e., harvesting, road construction/upgrading, and transportation operations) as well as their individual sustainability performances (economic, environmental and social aspects) in the allocation process. Moreover, this approach highlights the conditions under which the allocation ensures the stability of the configuration of the coalitions through a coalitional stability analysis. The proposed approach attempts to capture collaboration benefits and mills’ individual performances in the allocation process, while promoting equity among them. The coalitions of the case study overlap and thus, the concept of coalition configuration value is used to measure the marginal contribution of each mill to the cost savings. In particular, a methodology is proposed for the estimation of this value based on real data. The results of this study demonstrate that the allocation honors the efforts made by mills, both individually and collectively. In addition, it stimulates them towards a sustainable resource management relationship.

Cooperative target allocation for air-sea heterogeneous unmanned vehicles against saturation attacks

This paper proposes a cooperative target allocation method for efficiently utilizing air-sea heterogeneous unmanned vehicles to counter saturation attacks by low-cost UAVs. Specifically, a bilevel model that combines the advantages of heuristic algorithms and the coalition formation game (CFG) is constructed by integrating unmanned vehicles' motion and attack attributes. The upper layer model aims to utilize the advantages of the heuristic algorithm to generate a feasible target allocation scheme in a shorter time. A genetic algorithm constrained by inheritance conditions (GAC) is proposed to solve the problem of the low efficiency of traditional genetic algorithms in solving the upper model. The lower layer model is established based on a coalition formation game, which aims to continuously and stably optimize the target allocation scheme. A search method based on mobile players is designed to form a stable coalition structure faster when the number of unmanned vehicles is enormous. Simulation results show the feasibility and superiority of the algorithm proposed in this paper in dealing with allocation tasks of different complexity.

FedLaw: Value-Aware Federated Learning With Individual Fairness and Coalition Stability

FedLaw: Value-Aware Federated Learning With Individual Fairness and Coalition Stability

Accelerated K-Serial Stable Coalition for Dynamic Capture and Resource Defense

Accelerated K-Serial Stable Coalition for Dynamic Capture and Resource Defense

Designing stable coalition structures for international environmental agreements

Designing stable coalition structures for international environmental agreements

Interparental Conflict and Early Adolescent Depressive Symptoms: Parent-Child Triangulation as the Mediator and Grandparent Support as the Moderator

A notable ambiguity persists concerning whether distinct forms of parent-child triangulation (unstable coercive coalition, stable coalition, detouring-attacking, detouring supportive, parentification) might mediate the association between interparental conflict and early adolescent depressive symptoms similarly within the context of Chinese Confucianism. Filling this research gap, this study aimed to examine the mediating role of the five dimensions of parent-child triangulation in the association between interparental conflict and early adolescent depressive symptoms, as well as the moderating effect of grandparent support on this mediating pathway. Data were drawn from a sample of 761 Chinese adolescents (Mage = 12.82 ± 0.47, 49.1% girls). Structural equation model analyses indicated that unstable coercive coalition, stable coalition, and detouring-attacking behaviors partially mediated the association between interparental conflict and adolescent depressive symptoms, while detouring-supportive behaviors and parentification did not demonstrate such mediating effects. Unlike Western societies, a negative correlation was observed between interparental conflict and parentification in the context of China. Grandparent support mitigated the adverse effects of both interparental conflict and the unstable coercive coalition on early adolescent depressive symptoms.

Coalitional stability in matching problems with externalities and random preferences

We study coalitional stability in matching problems with externalities, including marriage markets, roommate problems, and Shapley-Scarf housing markets as particular cases. When preferences are randomly determined, the probability of having a coalitionally stable solution is positively affected by three factors: the prudence of coalitions when evaluating a deviation, the social connectedness of those that can react to it, and the incidence of externalities in preferences. At the same time, this probability is negatively affected by the number of agreements that agents can implement to block a matching. In this context, if agents have a limited capacity to organize themselves into large coalitions, then coalitional stability holds asymptotically even when individuals become less and less prudent as the population grows.

The Stackelberg vs. Nash-Cournot Folk-theorem in international environmental agreements

A commonly reported result in the literature on international environmental agreements (IEAs) is that if coalition members act as Stackelberg leaders (Stackelberg scenario) this leads to larger stable coalitions than if signatories act simultaneously with non-signatories (Nash-Cournot scenario). This result has been taken for granted, a kind of Folk-theorem, even though it has been proven at best for specific payoff functions, and very often the conclusion is only based on simulations. We prove the Stackelberg vs. Nash-Cournot Folk-theorem based on a generic payoff function for a public good provision game.