Cooperative Game Theory Methods Research Articles

Cooperative game theory methods for determining text complexity

We propose a method for estimating the complexity of texts based on the methods of cooperative game theory. The players in this game are the lengths of words in the text. The game itself is represented as a voting game in which the value of a player is determined by the number of coalitions in which the player is key. The ranks of the players are formed by computing the Shepley—Schubik value or the Banzaf index in a voting game with a given voting threshold. Thus, a vector of Shepley—Schubik or Banzaf values is assigned to each text. After that, the vector space is used to rank the texts in terms of complexity based on the expert evaluations obtained in this domain.

Bargaining Power in Cooperative Resource Allocations Games

Cooperative game theory provides an appropriate framework to assess the likelihood of conflict resolution, encourage cooperation among parties, and determine each party’s share in resource sharing conflicts. In calculating the fair and efficient allocation of the incremental benefits of cooperation, cooperative game theory methods often do not consider the exogenous bargaining powers of the players based on factors, that are external to the game, such as their political, economic, and military powers. This study reformulates three well-known cooperative game theory methods, namely, Nash-Harsanyi, Shapley, and Nucleolus, to account for the exogenous bargaining powers of the players in cooperative games. Using the Caspian Sea international conflict as an example, this paper shows how the negotiators’ exogenous bargaining power can change the outcome of resource sharing games. The proposed weighted cooperative game theory approach can help determine practical resolutions for real-world conflicts in which the exogenous powers of players can have a significant influence on the outcome of negotiations.

Optimizing hydropower generation and sediment transport in Yellow River basin via cooperative game theory

The complicated relationship between water and sediment in the Yellow River Basin (YRB) makes it imperative for reservoir stakeholders to game with each other to balance the short-term and long-term benefits. This paper proposes an integrated model to analyze the cooperation opportunities for major reservoir stakeholders engaged with the Longyangxia, Liujiaxia, Wanjiazhai, Sanmenxia, and Xiaolangdi reservoirs on the YRB mainstream. Multiple benefits are considered, including flood control, water supply, hydropower generation, and sediment trapping. Non-cooperation and cooperation scenarios are compared in this study. The effect of flow and sediment conditions on the incremental benefit of cooperation is examined, which shows that the systematic incremental benefit is larger when the YRB is dryer and sediment concentration is higher. Basin-wide cooperation is especially beneficial when the inflow peak comes earlier and the streamflow process is more fluctuating. Cooperation of reservoir stakeholders in a normal year (2019) can bring more incremental benefit (i.e., $22.57 million) in contrast to the non-cooperation scenario. Longyangxia, Liujiaxia, and Wanjiazhai reservoirs contribute most to the grand cooperation by implementing optimal operation for downstream stakeholders. Three cooperative game theory methods (Shapley value, Gately point, and Nash–Harsanyi solution) are employed to find possible benefit-sharing solutions. Based on cooperative game theory, the results demonstrate the core of basin-wide cooperation in the Yellow River is negligible due to the negative externality effect, implying more measures are needed by the government or non-profit organization to maintain the stability of grand coalition, i.e., water resources utilization control and external compensation. The results also show that Shapley value could be used to reallocate the incremental benefits in the grand cooperation.

Modeling and Comparative Analysis of Multi-Agent Cost Allocation Strategies Using Cooperative Game Theory for the Modern Electricity Market

The electrical market scenario has changed drastically in the last decade. In the presence of increased competition and less tolerant players, more sophisticated methods are required to balance the diversity and differential pricing while promoting cooperation among the agents. In the monopolistic environment, the central utility incurred the total cost of the transmission expansion. But as the current scenario demands, there are several public and private market players. The growth will benefit all the players, so the total cost in transmission expansion can be divided among players as per the benefit received by each player. In this paper, a transmission system expansion planning problem in the cooperative environment using cooperative game theory (CGT) is framed for the power sector, in which various players can cooperate in a coordinated manner to maximize their benefit but ultimately strengthen the power grid. In this paper, we have modeled, analyzed and compared various cost allocation methods of cooperative game theory specifically for the cost allocation in a transmission expansion planning problem. The present work focuses on forming coalitions to calculate the costs using the forward search and frog leap optimization approach. We have compared the SCRB, BSV, ENSC, and ACA methods for transmission expansion planning while attempting to satisfy the axioms. We have also observed that bilateral Shapely value efficiently allocated the costs due to its decentralized approach and the sequencing of coalition formations to achieve the best possible cost allocations.

The Multiport Berth Allocation Problem with Speed Optimization: Exact Methods and a Cooperative Game Analysis

We consider a variant of the berth allocation problem—that is, the multiport berth allocation problem—aimed at assigning berthing times and positions to vessels in container terminals. This variant involves optimizing vessel travel speeds between multiple ports, thereby exploiting the potentials of a collaboration between carriers (shipping lines) and terminal operators. Using a graph representation of the problem, we reformulate an existing mixed-integer problem into a generalized set partitioning problem, in which each variable refers to a sequence of feasible berths in the ports that the vessel visits. By integrating column generation and cut separation in a branch-and-cut-and-price procedure, our proposed method is able to outperform commercial solvers in a set of benchmark instances and adapt better to larger instances. In addition, we apply cooperative game theory methods to efficiently distribute the savings resulting from a potential collaboration and show that both carriers and terminal operators would benefit from collaborating.

Cooperative game theory methods for text ranking

A method of ranking the corpus of texts of a news portal, based on measures of graph centrality, is proposed. Each text is assigned a vertex of a certain graph, and its structure is determined based on the semantic connectivity of the texts. As a measure of centrality, the Myerson value is used in a cooperative game on a graph, where the number of simple paths in a subgraph of a certain length m is chosen as a characteristic function For different values of m, the ranking based on the Myerson value will be different. For the final ranking, it is proposed to use the ranking procedure based on the tournament matrix. The operation of the ranking algorithm is illustrated by numerical examples related to a specific news porta.

Robust cooperative planning of relief logistics operations under demand uncertainty: a case study on a possible earthquake in Tehran

Nowadays, the study of disasters such as earthquakes and their consequences, specifically in metropolises such as Tehran, has attracted significant attention. Allocating relief goods to distribution centres before the earthquake and providing relief services to the injured can reduce the fatality rate. Therefore, it seems quite necessary to present a certain routing and allocation scheduling model of relief vehicles to serve the injured. In this research, a mathematical model was proposed to minimise the unmet demands and transportation costs of relief vehicles and in the affected areas. Regarding the inherent uncertainties of disasters, we developed a robust scenario-based optimisation model for relief logistics networks to reduce the risk of fatality and provide near-optimal solutions for different possible disaster scenarios. We showed that the proposed cooperation plan produces a situation with additive supper property, which means that this type of cooperation will finally lead to a greater incentive for aid agencies to form larger coalitions. Furthermore, we proposed a set of cooperative game theory methods to distribute the cost-saving of the cooperation fairly.

A novel cooperative model in the collection of infectious waste in COVID-19 pandemic

PurposeProduction of waste has been increased exponentially due to world industrialization and urban and machine life expansion. On the other hand, the outbreak of the COVID-19 coronavirus quickly became a global crisis. This crisis has added a large amount of waste to urban waste. The purpose of this study is to create cooperation between municipal waste collector contractors.Design/methodology/approachThus, a mathematical model is proposed under uncertain conditions, which includes the volume of municipal waste and infectious waste including personal protective equipment and used equipment for patients. To reduce total costs, the results are evaluated with four cooperative game theory methods such as Shapley value, t value, core center and least core. Ultimately, the saved cost by cooperation in each coalition is allocated fairly among the contractors. Finally, a comparison was made between the solution methods based on the value of the objective function and the solution time.FindingsThe results indicate that the proposed cooperative method increases cost savings and reduces the fine of residual waste. Therefore, it can be mentioned that this kind of cooperation would finally result in more incentives for contractors to form larger coalitions. Genetic algorithms were used to solve the large-scale model.Originality/valueThe proposed model boosts the current understanding of waste management in the COVID-19 pandemic. The paper adds additional value by unveiling some key future research directions. This guidance may demonstrate possible existing and unexplored gaps so that researchers can direct future research to develop new processes.

Cooperative Game Theory Methods in the Analysis of Economic and Political Interaction at the International Level

The main attention is focused on the application of the methods of the theory of cooperative games to the analysis of the relationship between the leading actors in international politics, or, as they say, the centers of power. One of the speci c features of the modern world is the "triple type" of conflicts. Namely, at different levels of relationships, con ict situations with three participants (players) are often observed. Such situations are objectively characterized by the formation of possible paired coalitions, rejecting the third. The main idea of the proposed approach is the transition from cooperative games with deterministic values of characteristic functions to their counterparts with stochastic values. One of the possible concepts of solutions for stochastic cooperative games is associated with the extension of the ideas of the bargaining set to them. Problems of development and interpretation of this concept in the case of a triple conflict of international centers of power. An essential advantage of this approach is the possibility of meaningful interpretations of the significance level, at which the conditions for the rationality of the shares of the players should be ensured, taking into account the non-determinism of their utilities given by the characteristic function.

Cooperative cellular manufacturing system: a cooperative game theory approach

In the cellular industry, the components of products are increasingly being manufactured by multiple companies, which are distributed across different regions resulting in increased production costs. Here, a cooperative cellular manufacturing system is introduced to decrease these costs. A mathematical programming model has been proposed, which evaluates the production cost when companies work independently and the model is then extended to consider coalitional conditions in which the companies cooperate as an integrated cell formation system. A key question that arises in this scenario is how to arrange the cells and machines of multiple companies when their cell formation systems are designed cooperatively. Through a realistic case study of three high-tech suppliers of the Mega Motor Company, we show that these companies can reduce the costs through a cooperative cellular manufacturing system. We then compute the cost saving of each coalition of companies obtained from cooperation to get a fair allocation of the cost savings among the cooperating firms. Four cooperative game theory methods including Shapley value, τ -value, core-center, and least core are proposed to examine fair sharing of cost saving. A comprehensive analysis of the case study reveals important managerial insights.

Research on a Dynamic Decision Mechanism of Demand Oriented Supply Chain Cooperation Behavior

To solve the problem of supply chain management and decision-making under the restriction of the government and social group, we use the cooperative game theory method to seek a way to develop the enterprise. According to the general market competition in game analysis for product manufacturing enterprises as representatives for further discussion under the constraints of the government and social consumer groups, we examine the dynamic decision-making process of supply chain management, the attitudes adopted by the enterprises toward the government and consumer groups in the game for obtaining greater benefits, and the development of enterprises for providing creativity as well as theory and methodology.

Possibility of cooperative management in groundwater resources using an evolutionary hydro-economic simulation-optimization model

Groundwater as an open-access and a common pool resource (CPR) among several beneficiaries faces overexploitation especially in arid and semi-arid regions. To tackle such problems, cooperative management method using game theory concepts could be considered as an effective approach in operating a CPR. This study examines the effect of cooperation and internalization of environmental damages on managing the groundwater resources in Namdan aquifer located in Fars province, Iran. For this purpose, an evolutionary hydro-economic simulation-optimization model has been developed and various cooperation and environmental damages internalization scenarios have been considered to the study area over a planning horizon of 30 years. Continuous ant colony optimization (CACO) algorithm, which is an innovative application in this area of study has been applied to the simulation- optimization model. Some cooperative game theory methods have been used to allocate the obtained net benefits. The results indicate that under the full-cooperation scenario, the highest value of the sum of net benefits has been gained for any value of environmental damages. Moreover, internalizing the environmental damages has caused increase in the sum of net benefits among all cooperation scenarios. A sensitivity analysis has been conducted to assess the effect of changing the environmental damages value and also the importance factor of extraction externalities. The results of these analysis indicate that the cooperation conditions are independent of the value of environmental damages and also the intensity of extraction externalities. The methodology presented in this study provides water resource managers with a cooperative management platform in order to evaluate the possibilities of sustainable development of groundwater resources in more realistic conditions. The application of an efficient evolutionary algorithm provides a variety of realistic problems with an opportunity to overcome the limitations of traditional optimization techniques.

Water benefits sharing under transboundary cooperation in the Lancang-Mekong River Basin

Rapid economic development and population growth in the Lancang-Mekong River Basin makes it imperative for water resources to be used fairly and efficiently among all stakeholders. This paper proposes an integrated model framework to assess the water benefits sharing schemes among the five stakeholders in the basin, namely, China, Thailand, Laos, Cambodia, and Vietnam. Three objectives are considered for this assessment—hydropower (HP), eco-index (EI), and agricultural water use (AW). The hydrologic model, optimization model, and cooperative game theory methods are jointly used to analyze the water benefits of stakeholders under different scenarios. According to the model, cooperation can bring more incremental benefits in dry years when water resources are scarce. Three cooperative game theoretical methods, namely, the Shapley value, the Gately point, and the Nash–Harsanyi solution, are employed to find the possible benefit sharing solutions. The results show that China and Laos need to operate their reservoirs for downstream countries’ beneficial uses under cooperation, and thus, compensation by reallocating the incremental benefit from cooperation is necessary no matter which method is used. It is found that all of the future damming plans would enhance the basin-level cooperation in most cases. In particular, according to the analysis, damming in the basins of the Sesan, Srepok, and Sekong rivers would have more effect than damming in the upper Lancang-Mekong River Basin after 2030. Based on some verified assumptions, the results of this paper can offer real-world preferences, but the uncertainties need to be further explored.

Fair gain allocation in eco-efficient vendor-managed inventory cooperation

Transportation is not always organised efficiently, which causes unnecessary costs and CO2 emissions. Vendor-managed inventory (VMI) has been suggested as a form of cooperation that can reduce economic and environmental impacts of transportation and consequently improve eco-efficiency of the supply chain. Establishing viable forms of VMI cooperation requires a fair distribution of the cooperation's economic benefits. Cooperative game theory (CGT) research is used to fairly allocate both benefits and costs. However, the environmental contribution of partners has often been ignored in the benefit allocation. In this study, the Shapley value (a commonly used CGT method) is used to share the monetary gains in a way that reflects the partners' contributions to cost and emissions savings. The method is applied to evaluate the allocation of economic and environmental benefits of vendor-managed inventory between cooperating supermarket chains in the Netherlands. The findings show that there is a set of eco-efficient solutions resulting in lower costs and CO2 emissions compared to the current situation. For each of the eco-efficient solutions, the relative importance of saving costs and of saving emissions was quantified, and based on the importance weights, a cost allocation was found. For all partners that contribute to saving both cost and CO2 emissions, this approach results in cost savings, and therefore, the approach can be considered fair. Also, this approach helps to stimulate long-term eco-efficient forms of cooperation.

Tournament solutions based on cooperative game theory

This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to construct a characteristic function via the filled ballot paper profile of voters. The Shapley value serves as the ranking method. The winner is the candidate having the maximum Shapley value. And finally, we explore the properties of the designed ranking procedure.

Cooperative aggregate production planning: a game theory approach

Production costs in general, and workforce and inventory costs in particular, constitute a large fraction of the operating costs of many manufacturing plants. We introduce cooperative aggregate production planning as a way to decrease these costs. That is, when production planning of two or more facilities (plants) is integrated, they can interchange workforce and products inventory; thus, their product demands can be satisfied at lower cost. This paper quantifies the cost saving and synergy of different coalitions of production plants by a new linear model for cooperative aggregate planning problem. The developed approach is explicated with a numerical example in which inventory and workforce levels of different coalitions of facilities are evaluated. Afterward, a key question would be how the cost saving of a coalition should be divided among members. We tackle the problem using different methods of cooperative game theory. These methods are implemented in the numerical example to gain an insight into properties of the corresponding game results.

Network partitioning algorithms as cooperative games

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolutions. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for approaches based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling.

Sustainability risk management in a cooperative environment under uncertainty

PurposeThis study considers a project scheduling model to assess the project risks and the impacts on project sustainability when subcontractors collaborate under uncertainty. Moreover, some allocation methods are applied for fair allocating utility of the project and supper-additivity, stability and satisfaction level of each coalition. Finally, sustainability concept is considered in risk assessment in all coalitions.Design/methodology/approachThe proposed mathematical programming model evaluates project risks when the subcontractors cooperate with each other by sharing their limited resources. Then, some cooperative game theory methods are applied for fair allocation of net present value, of the cooperation and finally sustainability aspects (economic, social and environmental) are investigated in risk assessment for each possible coalition.FindingThe results of the proposed model indicate that the subcontractors can increase their profit by 10 per cent ($14,028,450 thousand) and save the equilibrium between sustainability aspects especially in grand coalition. It means that subcontractors do not have incentive to leave the coalition and the supper-additive property is feasible. Furthermore, risk assessment shows that project risks have less impact on subcontractor profits when they cooperate with each other.Originality/valueSustainability aspects may be investigated in project management in previous studies, but the authors study sustainability indicators when subcontractors form a coalition and share their resources in response to the risks of availability to resources and delay in completing the project under uncertainty.

Cooperation of advertising companies in social networks: A graph and game theory approaches

Abstract Advertisement in companies that are active in social network is becoming a key success factor these days. The cooperative advertising enables companies to improve effectiveness of the advertisement efforts. In this research, we first present a mathematical model to quantify the profit of cooperation between the companies in a network. Afterwards, cooperative game theory methods such as Shapley value, Core-center, Least core, and τ-value are proposed to distribute benefits of the cooperative advertisement of the companies in the social networks. A numerical example of a simple social network with three advertising companies is presented to evaluate results of the models. It is shown that the profit obtained from coalition is greater than individual profits of the members. In this regard, fair allocation of the extra profit among companies ensures their satisfaction and long-term cooperation.

Developing new scenarios for water allocation negotiations: a case study of the Euphrates River Basin

Abstract. Mismanagement and uneven distribution of water may lead to or increase conflict among countries. Allocation of water among trans-boundary river neighbours is a key issue in utilization of shared water resources. The bankruptcy theory is a cooperative Game Theory method which is used when the amount of demand of riparian states is larger than total available water. In this study, we survey the application of seven methods of Classical Bankruptcy Rules (CBRs) including Proportional (CBR-PRO), Adjusted Proportional (CBR-AP), Constrained Equal Awards (CBR-CEA), Constrained Equal Losses (CBR-CEL), Piniles (CBR-Piniles), Minimal Overlap (CBR-MO), Talmud (CBR-Talmud) and four Sequential Sharing Rules (SSRs) including Proportional (SSR-PRO), Constrained Equal Awards (SSR-CEA), Constrained Equal Losses (SSR-CEL) and Talmud (SSR-Talmud) methods in allocation of the Euphrates River among three riparian countries: Turkey, Syria and Iraq. However, there is not a certain documented method to find more equitable allocation rule. Therefore, in this paper, a new method is established for choosing the most appropriate allocating rule which seems to be more equitable than other allocation rules to satisfy the stakeholders. The results reveal that, based on the new propose model, the CBR-AP seems to be more equitable to allocate the Euphrates River water among Turkey, Syria and Iraq.