Value Of Coalition Research Articles

A partition-graph restricted cooperative game with incomplete information

In a partition-graph restricted cooperative game with incomplete information, it is assumed that a prior coalition takes part in the grand coalition N in form of communication structure. Before the grand coalition is formed, all the players participate in the cooperation just by communication structure. Hence, a new cooperative game with communication structure (a restricted game for short) is formed. In this study, a new value of a restricted game is proposed, which is defined by the Myserson value and the Shapley value. It is proved that the added value of grand coalition is distributed by a certain ratio (i.e., the Shapley value). By generalized the distribution ratio, a further extension of the proposed value is gotten, i.e., the weight extended value. This weight extended value is unique based on restricted component efficiency, weight fairness, weight symmetric across coalitions, null coalition property and restricted linearity.

Equilibrium analysis in majority-based coalitional bargaining games

This paper introduces majority rule into coalitional bargaining games, adapting traditional models that rely on unanimous consent to more accurately mirror decision-making processes in real-world scenarios. We introduce a majority-based coalitional bargaining game (MBCBG), wherein coalitions pass proposals via majority votes. Our analysis of the stationary subgame perfect equilibrium (SSPE) not only establishes the necessary and sufficient conditions for SSPE strategy profiles but also confirms the existence of no-delay SSPEs in MBCBGs. We further delve into symmetric MBCBGs, delineating conditions that ensure equitable outcomes for homogeneous players. Furthermore, we provide a necessary and sufficient condition for the formation of the grand coalition under SSPEs. Additionally, we briefly explore how asymmetries in coalition values, proposal probabilities, and voting weights may influence both the dynamics of coalition formation and the expected equilibrium payoffs.

GT-CAM: Game Theory based Class Activation Map for GCN.

Graph Convolutional Networks (GCN) have shown outstanding performance in skeleton-based behavior recognition. However, their opacity hampers further development. Researches on the explainability of deep learning have provided solutions to this issue, with Class Activation Map (CAM) algorithms being a class of explainable methods. However, existing CAM algorithms applies to GCN often independently compute the contribution of individual nodes, overlooking the interactions between nodes in the skeleton. Therefore, we propose a game theory based class activation map for GCN (GT-CAM). Firstly, GT-CAM integrates Shapley values with gradient weights to calculate node importance, producing an activation map that highlights the critical role of nodes in decision-making. It also reveals the cooperative dynamics between nodes or local subgraphs for a more comprehensive explanation. Secondly, to reduce the computational burden of Shapley values, we propose a method for calculating Shapley values of node coalitions. Lastly, to evaluate the rationality of coalition partitioning, we propose a rationality evaluation method based on bipartite game interaction and cooperative game theory. Additionally, we introduce an efficient calculation method for the coalition rationality coefficient based on the Monte Carlo method. Experimental results demonstrate that GT-CAM outperforms other competitive interpretation methods in visualization and quantitative analysis.

Coalitional Value of Formidable Men in Hostile and Desperate Ecologies

Coalitional Value of Formidable Men in Hostile and Desperate Ecologies

An efficient solidarity value for interval cooperative games

This paper proposes an efficient interval solidarity value that operates well for interval cooperative games. In addition to the axioms of symmetry, efficiency, and additivity, this value also satisfies two new axioms, namely, interval-egalitarian A-null player and interval differential marginality. The interval-egalitarian A-null player axiom equally divides the result of the difference between the grand coalition value and the sum of the solidarity value of players in the degenerate interval game among A-null players. The interval differential marginality axiom is an interval version of the Casajus differential marginality axiom. This property states that the difference in the interval solidarity value of two players is determined by the difference between their average marginal contributions in the degenerate interval game. Eventually, the efficiency results and applicability of the proposed approach are compared with those of the other methods.

Fair Allocation in Crowd-Sourced Systems

In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. We use the framework of a Shapley allocation which is regarded as a fundamental method of computing the fair share of all participants in a cooperative game when the values of all possible coalitions could be quantified. To quantify the value of all coalitions, we define a class of value functions for crowd-sourced systems which capture the contributions of the founders and the crowd plausibly and derive closed-form expressions for Shapley allocations to both. These value functions are defined for different scenarios, such as the presence of oligopolies or geographic spread of the crowd, taking network effects, including Metcalfe’s law, into account. A key result we obtain is that under quite general conditions, the crowd participants are collectively owed a share between 12 and 23 of the total value of the crowd-sourced system. We close with an empirical analysis demonstrating the consistency of our results with the compensation offered to the crowd participants in some public internet content sharing companies.

Coalition Game Based Distributed Clustering Approach for Group Oriented Unmanned Aerial Vehicle Networks

Clustering is an effective solution to improve the management efficiency of large-scale systems. One one hand, UAVs performing the same task have a similar moving tendency. One the other hand, the network topology of the UAV swarms is dynamically changing. Considering the above two aspects, our main contributrons are designing a group-oriented distributed clustering algorithm based on the coalition game that couples task attributes and communication attributes. The clustering goal is to divide UAVs performing the same task into one cluster and make each cluster have more UAVs under the cluster size limits, thus improving communication efficiency. The proposed algorithm comprehensively considers the task group information and communication link stability as the coalition value. UAVs decide whether to leave their current coalition based on coalition values. Through periodic parallel switch operations selection, UAVs are divided into the desired clustering structure. Simulations verify that our clustering algorithm is effective and better than the existing ones, especially in communication link stability, cluster numbers, and load balance.

On an axiomatization of the grey Banzhaf value

<abstract><p>The Banzhaf value with grey data is a solution concept in cooperative grey games that has been extensively studied in the context of operations research. The author aims to define the traits of the Banzhaf value in cooperative grey games, where the values of coalitions are depicted as grey numbers within intervals. The grey Banzhaf value is defined by several axioms, including the grey dummy player, grey van den Brink fairness, and grey superadditivity. By presenting these axioms, this investigation contributes novel insights to the axiomatic characterization of the grey Banzhaf value, offering a distinct perspective. Finally, the study concludes by presenting applications in cooperative grey game models, thereby enriching the understanding of this concept.</p></abstract>

Contextual factors that heighten interest in coalitional alliances with men possessing formidable facial structures

Individuals use facial width-to-height ratio (fWHR) to infer men's formidability. We hypothesized that fWHR assessments would form a basis for men's coalitional value, with high-fWHR men being valuable in roles requiring physical strength. Five studies (N = 1323) tested how perceptions of formidability influence coalitional decisions. In addition to replicating previous findings indicating a preference for high-fWHR men in tasks requiring strength (Study 1), the formidability inference most associated with this high-fWHR preference was perceived strength and not aggressiveness (Studies 2a, 2b). Two pre-registered studies showed that activating competitive motivations increased preferences for high-fWHR allies (Study 3), though this preference appeared driven by a tolerance for high-fWHR men rather than an interest (Study 4). Findings provide evidence for how inferences of fWHR shape interpersonal preferences based on social contexts.

Cooperative Relative Localization for UAV Swarm in GNSS-Denied Environment: A Coalition Formation Game Approach

Unmanned aerial vehicle (UAV) swarms require accurate relative localization to safeguard flight missions in the global navigation satellite system-denied environment due to a lack of absolute position information. The existing work of relative localization faces challenges, such as the ranging information loss and the low localization frequency caused by long-distance ranging and large-scale characteristic of the UAV swarm. This article proposes a clustering-based cooperative relative localization scheme for UAV swarm, which contains a two-level framework: inter/intra-cluster localization. In order to investigate the tradeoff between intracluster cooperation and intercluster packet loss, the clustering-based problem is constructed as a coalition formation game (CFG) model. Given the designed coalition value, preference relation, and the coalition formation principles, it is proved that the proposed CFG model has a Nash stable partition. The designed coalition formation algorithm includes coalition heads and beacon drones selection mechanism. Simulation results show that the proposed CFG algorithms shorten the ranging time compared with global localization and achieve better localization performance (localization error and success rate) than contrast algorithms.

Characterization of a value for games under restricted cooperation

The object of this paper is to study restricted cooperative games, that is, cooperative games for which the worth of some coalitions is unknown. We consider a value for these restricted cooperative games whose definition is based on the Harsanyi’s dividends approach, and can therefore be seen as an extension of the Shapley value. We provide a characterization of this value with three axioms: Carrier, Symmetric-partnership and Additivity, which are similar to those proposed by Shapley (in: Kuhn and Tucker (eds) Contributions to the theory of games, Princeton University Press, Princeton, 1953). In addition, we characterize this value on the subclass of restricted cooperative simple games. Finally, we apply this value for restricted cooperative games to analyze the power distribution of the Catalonian Parliament in 1980 and compare the results with those of the coalitional value in Carreras and Owen (Math Soc Sci 15:87–92, 1988).

Sharing congestion management costs among system operators using the Shapley value

With energy generation becoming increasingly decentralized, the need for congestion management across grid voltage levels is also increasing. To enable fair sharing of congestion costs among grid operators, these costs must be allocated to congested grid elements. We propose using the Shapley value for this purpose. The Shapley value is a cooperative game theory concept that was developed to share a total surplus generated by a coalition of players between the players based on their marginal contributions to the coalition. We apply this concept to share the costs of congestion management between grid elements based on their contributions to overall congestion management costs. To reduce the computational complexity of the Shapley value, we introduce two novel simplification approaches and compare them to existing methods using a numerical example based on CIGRE benchmark grids. The first method exploits the fact that the characteristic function for the congestion costs is obtained from an optimal power flow computation (i.e., a constrained optimization problem). It utilizes knowledge about which constraints are non-binding in the optimization to derive the values of related coalitions without calculating them. The second method takes advantage of the fact that the congestion management cost-allocation game is monotone and derives the values of coalitions based on this property. Both methods are implemented and compared to sampling. Using the first method, we are able to reduce computational complexity to less than 20% of that of the original problem while maintaining exact results. Our second approach is not dependent on detailed knowledge of the underlying optimization problem and can reduce the computational time by almost half with exact results and much further when compromising precision. While the methods are presented through an application example, they can be applied to other games with similar properties.

Payoff Distribution in Robust Coalitional Games on Time-Varying Networks

In this paper, we consider a sequence of transferable utility (TU) coalitional games where the coalitional values are unknown but vary within certain bounds. As a solution to the resulting family of games, we formalise the notion of Our main contribution is to design two distributed algorithms, namely, distributed payoff allocation and distributed bargaining, that converge to a consensual payoff distribution in the robust CORE. We adopt an operator-theoretic perspective to show convergence of both algorithms executed on time-varying communication networks. An energy storage optimization application motivates our framework for coalitional games.

Handoff optimization for joint base station association and power control in uplink non‐orthogonal multiple access small cell networks

AbstractThis article investigates the handoff optimization in an uplink non‐orthogonal multiple access‐based small cell network (SCN) with successive interference cancellation that takes both the base station (BS) association and power control into consideration. Due to user mobility and varying communication environment, it is important to associate a user with the proper BS and control its transmit power by considering the user mobility for the SCNs. To overcome overly frequent re‐association and handoffs between BSs, a novel joint optimization of handoff, BS association, and total transmit power is presented that maximizes the system‐wide and handoff utilities and minimizes power consumption simultaneously. We define the handoff utility function by considering the BS association in each time frame with the previous time frame. Then, we formulate two inter‐related optimization problems under the minimum average‐rate and maximum allowable transmit power of mobile users (MUs) constraints. The designed optimization problems are combined through the weighted sum method into a single‐stage optimization problem. The transformed problem is solved by adopting the coalition formation game and primal decomposition theories. We design the coalition value function by collectively considering the handoff number of each BS in every time frame, transmit power of all MUs, and the number of associated MUs to every BS. The simulation results show the efficiency of the proposed handoff algorithm in comparison to another BS association algorithm in terms of the number of handoffs.

Coalitional bargaining games: A new concept of value and coalition formation

We propose a new solution for coalition bargaining problems among n players that can form coalitions c generating heterogenous coalitional values ▪. The players' values vi and probability of coalition formation ▪ are given by: [Display omitted] where coalition c is chosen only if it maximizes the average gain ▪ and ▪. This solution is the strong Markov perfect equilibrium of a non-cooperative coalition bargaining game where players choose simultaneously the coalition they want to join followed by negotiations to split the surplus. The solution does not rely on the specification of a proposer recognition protocol. For majority voting games, the solution exhibits more inequality among the values of large and small parties and a concentrated equilibrium coalition formation distribution.

On the Online Coalition Structure Generation Problem

We consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size.
 Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value α. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.

Experimentally testing the impact of status threat on heterosexual men’s use of anti-gay slurs: A precarious manhood and coalitional value perspective

Experimentally testing the impact of status threat on heterosexual men’s use of anti-gay slurs: A precarious manhood and coalitional value perspective

Cooperative Games with Multiple Scenarios in Intuitionistic Fuzzy Environment

‎The main aim of this paper is to introduce the core and nucleolus notions of cooperative games with multiple scenarios in uncertain environment‎. ‎Taking imprecision of information into account‎, ‎we incorporate fuzzy coalition values‎, ‎which are represented by intuitionistic fuzzy numbers‎. ‎They can be applied as an appropriate approach to define a fuzzy set in the case that available information is not sufficient for defining an imprecise concept by means of a conventional fuzzy set‎. ‎The characteristic function of such games associates a coalition with a vector containing the intuitionistic fuzzy components‎. ‎The notion of expected interval is defined and computed for the intuitionistic fuzzy numbers‎. ‎Then‎, ‎an approach is proposed to transform the problem into a single-objective cooperative game with interval-valued payoffs‎. ‎The concepts of core and nucleolus are considered‎. ‎It is shown that the core is nonempty in these games‎. ‎A method is proposed to compute the nucleolus of such the problems‎. ‎Finally‎, ‎the validity and applicability of the approach are illustrated by a numerical example.

New results on egalitarian values for games with a priori unions

Several extensions of the equal division value and the equal surplus division value to the family of games with a priori unions have been proposed by Alonso-Meijide et al. [On egalitarian values for cooperative games with a priori unions. TOP. 2020;28:672–688]. In this study, we provide new axiomatic characterizations of these values. Furthermore, using the equal surplus division value in two steps, we propose a new coalitional value. The balanced contributions and quotient game properties generate a different modification of the equal surplus division value.

Pricing strategies of an oligopolist in federated cloud markets

In this paper, we study how an oligopolist influences the coalition structure in federated cloud markets. Specifically, we use cooperative game theory to model the circumstances under which a cloud provider prefers to join a cloud federation vis-a-vis consider taking a price offer made by an oligopolist. We consider two price offering strategies for an oligopolist: non-adaptive and adaptive. In non-adaptive strategy, an oligopolist makes a price offer to all the cloud providers simultaneously. It can be noted that the oligopolist can buy-out all the cloud providers by making a price offer which is equal to a core allocation and the total price offer made by the oligopolist is equal to the value of the grand coalition. In adaptive strategy, the oligopolist approaches the cloud providers one after another in a sequential manner. We show that by using the adaptive strategy, the oligopolist can buy-out all the cloud providers at a total price offer which is less than that of the non-adaptive strategy.