Cooperative Game Analysis Research Articles

Information Asymmetric Cooperative Game with Agreements Implemented by a Third Party

This paper introduces asymmetric information into the analysis of cooperative games with agreements implemented by a third party and establishes theoretical models of a one-time information asymmetric cooperative game with agreements implemented by a third party for the first time, using the methodology proposed in previously done research studying coalition formation and cooperative payoff distribution. In an information asymmetric cooperative game with agreements implemented by a third party, players may retain their own private information, and make decisions through their virtual games on the basis of their own information sets. This paper defines the virtual cooperative games of the players and demonstrates the equilibrium of the virtual cooperative game of a player; proposes the condition for the existence of the coalition equilibrium in an information asymmetric cooperative game with agreements implemented by a third party, defines and provides the existence proof of this coalition equilibrium when it does exist; defines the public choice game of a coalition on the strategic combination choice in a certain coalition situation, defines and provides the existence proof of the equilibrium of this game; examines the condition for the existence of the bargaining game on the distribution of the cooperative payoff of a coalition, defines and provides existence proof of the bargaining game, when the coalition members are allied or unallied in the bargaining game.

How can the recycling of power batteries for EVs be promoted in China? A multiparty cooperative game analysis

While electric vehicles (EVs) are developing at a high speed in China, the power battery market is facing a decommissioning peak. The problem is that the recycling situation of domestic power batteries is not ideal, partly due to neglect by consumers. By considering the recycling system, mode, and policy of China’s EV power batteries, we construct a tripartite evolutionary game model of the government, consumers and EV manufacturers; analyse the stable strategy adjustment mechanisms of tripartite participation in this recycling cooperation game; and simulate the tripartite evolutionary game. The results show that when the initial willingness of the government, consumers and EV manufacturers to recycle power batteries is not strong, the government takes the lead, driving EV manufacturers and consumers to participate in power battery recycling. When the government, consumers and EV manufacturers have medium or high levels of initial willingness, the government evolves and chooses a nonregulation strategy. In addition, by simulating the impact of changes in consumer-related influencing factors on this tripartite evolutionary game, we find that subsidies for recycling power batteries are a key factor affecting consumers’ strategy choices and that boosting recycling compensation for consumers can improve their enthusiasm to participate in such recycling. Therefore, to improve the recycling of power batteries for EVs, in terms of both efficiency and percentage of deployment, the Chinese government should strengthen public education on power battery recycling, further integrate informal recycling channels, and balance the distribution of profits among consumers for recycling compensation.

Game Analysis of Cooperation Between Entrepreneurial Users and Tiktok Platform

In the new era, Tiktok platform has attracted a large number of users with short video and live broadcast functions, forming a huge user group, and the platforms purchasing power has gradually increased, providing rich profit opportunities for entrepreneurial users. Tiktok realizes business value through the output of entrepreneurial users, and both parties achieve mutual benefit in the game. This paper mainly studies how Tiktok and entrepreneurial users can make better profits through game theory. The problem is analyzed by two aspects which are business model and game ecology of Tiktok platform and game relationship between Tiktok and entrepreneurial users. And the game is based on Nash equilibrium, through the study, we get the conclusion that the balance of Tiktok and senior users is increasing the service fees and reducing the cost of products and that of Tiktok and novice users is decreasing the service fees and raising the cost of products.

Stochastic evolutionary game analysis of food cooperation among countries along the Belt and Road from the perspective of food security

IntroductionIn recent years, the combination of the public health crisis and the climate crisis has greatly weakened the resilience of food systems. The Belt and Road food cooperation will make outstanding contributions to consolidate food security and reduce global poverty in countries along the Belt and Road.MethodsThis paper constructs a three-party stochastic evolutionary game model from the perspective of food security, distinguishes the difference between large and small countries by calculating the cereal self-sufficiency rate, which studies the cooperation strategy with the Belt and Road cereal large countries, cereal small countries and regulatory committees as the object. In addition, we introduce the Gaussian white noise characteristics to characterize the stochastic disturbance of the game system. Then we combine the mathematical derivation of the stochastic evolutionary game analysis with the simulation method, examine the effect of the stochastic disturbance factors on the cooperation, and find out the factors that affect the cooperation. And finally verifies the model and proves the reasonableness and practicability of the model.ResultsThe stochastic evolutionary game model analyzes the interaction of stochastic disturbance and influencing factors from a dynamic perspective, and the stability of evolution is related to the strength of Gaussian white noise. The level of effort of large cereal countries and the incentives of regulatory committees can have a positive impact, but high income in small cereal countries can lead to instability in the strategic choices of other players.DiscussionTaking the countries along the Belt and Road as the research object, Gaussian white noise is introduced to describe the stochastic external environment, discriminate the stability of the game system through stochastic differential equations, and analyze the influencing factors of the dynamic behavioral strategies of the parties in combination with simulation methods. To improve the capacity of national food security governance and help improve the resilience of the world food system.

Cooperative Game Analysis based on Country Size and Market Position

This paper studies the cooperative game theory, and analyzes the cooperative game with international scale and market position. From the perspective of evolutionary game theory, this paper discusses the preconditions for big and small countries to participate in regional economic cooperation and the stability conditions of economic cooperation. This paper combines cooperative game theory with regional economic integration, and the economic and political alliance among countries can be regarded as a cooperative game. In order to analyze the cooperation of member countries, the countries are divided into small countries and big countries according to their size and market position, and the replication dynamic equation is calculated, then the basic conditions of the strategy of big countries and small countries participating in regional economic alliance are obtained, and the strategy selection probability of participants under the conditions of equilibrium strategy and non-equilibrium strategy is analyzed. In addition, using evolutionary game theory and Jacobian matrix to analyze the stability of local equilibrium point, a reciprocal game model of regional economic cooperation between big and small countries is established. Through the research, it is found that the necessary condition for the formation of regional economic integration is the economic complementarity among the cooperative parties, and the sufficient condition is that the cooperative parties can coordinate the distribution of interests among themselves through effective consultation and finally reach a binding agreement on the distribution of interests, thus restricting each other's economic behavior.

Shapley Mapping and Its Axiomatizations in n-Person Cooperative Interval Games

Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution concept applied to interval games, by comparing it with the existing solution concept called the interval solution concept. Then, we define a Shapley mapping as a specific form of the solution mapping. Finally, it is shown that the Shapley mapping can be characterized by two different axiomatizations, both of which employ interval game versions of standard axioms used in the traditional cooperative game analysis such as efficiency, symmetry, null player property, additivity and separability.

Research on Evolutionary Game Analysis of Spatial Cooperation for Social Governance of Basin Water Pollution

Given that the two institutional arrangements of government regulation and market allocation cannot effectively solve the conflict between individual and collective interests in the process of water pollution control, this work presents a useful attempt on the third institutional arrangement of environmental governance—social governance—to overcome the dilemma. Based on common pool resource theory and multi-person prisoner game analysis framework, it incorporates environmental damage function, spatial network structure, and strategy update based on a learning mechanism into the analysis framework. In addition, it constructs a set of spatial cooperative evolution game models of basin water pollution social governance, so as to test the guarantee effect of the spontaneous collective action conditions of basin polluters on the long-term survival of the new system. This work adopts the Monte Carlo numerical simulation method to conduct the simulation experiment research. The experimental results show it is possible to successfully form collective actions entirely dependent on emitters, which yet requires a large initial scale of cooperation, that is, a majority of the emitter group autonomously abides by credible commitments. In this process, transparent full information and active organizational mobilization have a positive effect on the collective action development. The organic combination can better guide emitters to abide by credible commitments to achieve the optimal collective interests. The study results can provide a theoretical and practical reference for the social governance mechanism at a large-scale basin.

Unfair and Risky? Profit Allocation in Closed-Loop Supply Chains by Cooperative Game Approaches

Behavioral factors (i.e., risk aversion and fairness concern) are considered for profit allocation in a closed-loop supply chain. This paper studies a two-echelon closed-loop supply chain (CLSC) consisting of a risk-neutral manufacturer, a risk-averse fairness-neutral retailer, and a risk-neutral retailer having fairness concerns. Cooperative game analysis is used to characterize equilibriums under five scenarios: a centralized, a decentralized and three partially allied models. Analytical results confirm that even when factoring in retailers’ risk aversion and fairness concern, the centralized model still outperforms decentralized. This paper makes a numerical study on the effects of risk aversion and fairness concern on profit distribution under these five models. It reveals that the impact of the risk aversion parameter and fairness concern parameter is dynamic, not always positive or negative. These research results provide helpful insights for CLSC managers to find out available choices and feasible ways to achieve fair profit allocations.

Stochastic Game Analysis of Cooperation and Selfishness in a Random Access Mechanism

This paper introduces a general stochastic game analysis of a network scenario consisting of a mix of cooperative and non-cooperative players (i.e., users) under incomplete game information. Users access a shared channel using the Slotted ALOHA mechanism combined with ZigZag Decoding (SAZD). Cooperative players seek to optimize the global utility of the system (e.g., throughput, delay, loss rate) regardless of their individual interests, whereas non-cooperative players act selfishly and optimize their own benefits irrespective of the impact of this behavior on others and on the entire network system. The game equilibrium is characterized by the social optimum and the Nash equilibrium, where the former is adopted by cooperative players and the latter is the equilibrium strategy of non-cooperative players. We undertake a comparative study across two game scenarios with different levels of cooperation and selfishness. Our results generally show that the information possessed by a player can determine the outcome. Furthermore, our findings show that the network performance is strongly influenced by selfish behavior, which can lead to a significant disruption of the entire system. Finally, we show a possible scenario in which the network could greatly benefit from this selfish behavior thanks to the ZigZag scheme.

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.

Evolutionary Game Analysis of Competition and Cooperation of Green Technology Innovation among Enterprises under Government Incentive

Based on the situation of green technology innovation and development of enterprises, this paper studies the evolution of the competitive and competitive game relationship of green technology innovation among enterprises with different government incentives by establishing an evolutionary game model. Matlab software is used to numerically calculate the evolutionary path of the game between government and enterprises and the position change of equilibrium point. The dynamic evolution of collaborative innovation behavior and interaction among enterprises is discussed. The results show that in the process of green technology innovation, enterprises will be more inclined to green technology innovation cooperation only when they are fully "motivated". In the process of innovation and development of green technology among government enterprises, it has a very important influence. Under the reasonable supervision of the enterprise government, it is easier to optimize the allocation of innovative resources, effectively reduce the situation that enterprises have no green technology innovation cooperation, realize better control of innovation costs, and then bring double benefits of economic and social benefits through the development of technological innovation.

Games theory and strategic alliances: applications to British Russian partnership

PurposeThis conceptual paper examines the need for viable theoretical models of international learning alliances in the light of cooperative games and complexity in two distinguished educational settings. Game theory is used to demonstrate the need for the top managerial executives to acquire a detailed understanding of decision makers' behaviours and trigger the deployment of complex analytical methods. The paper scrutinizes Russia's pursued aggressive approach using shock therapy, also suggest the critical need to reform policy.Design/methodology/approachCombining the critical analysis of (1) cooperative games and (2) adaptive systems structures, a dependable model is derived, which sets the baseline for determining the role of costs and gains. The analysis is supported using a real-world example of an alliance between British University (the X and Y alliance) and Russian University. It also emphasizes the importance of both internal and external pressure variables closely connected with the cooperative games, adaptive system and shock therapy.FindingsTwo features of alliances have been emphasized. The first is the importance of informal relationships in the evolution of partnerships and of cooperation. This is a well-known factor in the success of any relationship. Especially in international partnerships, empathy at the individual level is perhaps necessary to bypass the influence of historical and cultural differences that are barriers at the macro level, preconditions rather than consequences of successful policies and contractual arrangements at the level of organizations and governments. The second feature is interdependence at the cost–benefit level and in the domain of decisions. The cooperation of both partners is required to realize payoffs.Practical implicationsThe implication of this paper is a guideline for regulators and policymakers designing worldwide alliances in higher education. In addition, this paper covers an interesting domain that could be of interest to organizations involved in forming strategic alliances, developing and re-engineering policies for strategic coalitions and setting future profitable payoff relationships within the contextual limitations of X and Y.Originality/valueThis paper creates new knowledge by concisely examining the meaning of strategic alliances in the context of the global education industry.

The impact of intermediaries on a negotiation: an approach from game theory

Standard approaches to model interaction networks are limited in their capacity to describe the nuances of real communication. We present a game theoretical framework to quantify the effect of intermediaries on the interaction between agents. Inspired by the seminal work Myerson (1977). on cooperative structures in cooperative games, we set the basis for multidimensional network analysis within game theory. More specifically, an extension of the point-arc game Feltkamp and van den Nouwe51 land (1992). is introduced, generalizing the analysis of cooperative games to multigraphs. An efficient algorithm is proposed for the computation of Shapley value of this game. We prove the validity of our approach by applying it to a intermediaries network model. We are able to recover meaningful results on the dependence of the game outcome on the intermediaries network. This work contributes to the optimal design of networks in economic environments and allows the ranking of players in complex networks.

Modelling and Verification Analysis of Cooperative and Non-Cooperative Games via a Modal Logic Approach

In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players (coalitions) due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analyzed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players’ actions and payoffs and analyzing Nash equilibriums. In this work, the cooperative and non-cooperative game problem is modeled by means of a modal logic formula. Then, using the concept of logic implication, and transforming this logical implication relation into a set of clauses, a modal resolution qualitative method for verification (satisfiability) as well as performance issues, for some queries is applied.

Computer Software Applied in Cooperative Game Analysis Using Myerson Value in the Probability Graph

With the development of economy and society, technology trading activities in China are increasingly frequent, science and technology intermediary is an important part of China’s technology trading market system, the cooperation among technology suppliers, technology demanders and technology intermediaries has become a major trend in technology trading market, however, there are many uncertainties in the process of tripartite cooperation. In order to better describe the situation of practical cooperation in technology trading, this paper introduces the Myerson value in the probability graph in cooperative game to analyze the profit distribution problem among technology supplier, technology intermediary and technology demander in technology trading market, and discusses the effect of utility distribution on the interests of all parties by using the relevant model, and makes a comparative analysis with the Myerson value in the general graph, Finally, some suggestions are put forward to promote the stability and sustainable development of the technology trading market.

Differential Game Analysis of the Green Innovation Cooperation in Supply Chain under the Background of Dual-Driving

Taking government environmental regulation and consumer’s green preference into a unified analytical framework, this study constructed a differential game model. With the joint effect of supplier and manufacturer green innovation efforts on the dynamic change of the product’s green level, it compared and analyzed the long-term dynamic equilibrium strategies of green innovation cooperation in a supply chain under decentralized and centralized decision-making situations. Accordingly, a scientific and reasonable profit-distribution contract was then proposed. On this basis, it further carried out a numerical simulation analysis on the dual-driving effects of the government and market. The results showed that the scientific and reasonable profit-distribution contract under the centralized decision-making situation, which was designed by using the Rubinstein bargaining game model, could effectively ensure that the supply chain members’ sharing profits would realize "Dual Pareto Improvements." With the increase of the environmental regulation’s intensity, the product’s green level kept rising and tended to be stable. However, the overall equilibrium profit of the supply chain was characterized by "U" fluctuation, which first descended and then ascended. In addition, the product’s green level, the green innovation investment and equilibrium (distributed) profits of supply chain members, and the overall profits of supply chain all increased with the consumers’ green preference.

Cooperative game analysis of coordination mechanisms under fairness concerns of a green retailer

This study discusses how a green retailer's fairness concerns affect product greenness and profit and explores how to distribute surplus profits under the fairness concerns using cooperative game theory. Research findings indicate that cooperation contributes to increasing channel profits and improving product greenness, but the fairness concerns are detrimental to them. The three proposed coordination mechanisms (SVM, NSM, and TVM) are feasible to ensure coalition stability, but their beneficiaries differ. NSM benefits a manufacturer, while SVM benefits retailers. Additionally, the green retailer's fairness concerns serve as distribution tools to narrow profit gaps between the manufacturer and the green retailer.

Multiplayer Allocations in the Presence of Diminishing Marginal Contributions: Cooperative Game Analysis and Applications in Management Science

We use cooperative game theory to investigate multiplayer allocation problems under the almost diminishing marginal contributions (ADMC) property. This property indicates that a player’s marginal contribution to a non-empty coalition decreases as the size of the coalition increases. We develop ADMC games for such problems and derive a necessary and sufficient condition for the non-emptiness of the core. When the core is non-empty, at least one extreme point exists, and the maximum number of extreme points is the total number of players. The Shapley value may not be in the core, which depends on the gap of each coalition. A player can receive a higher allocation based on the Shapley value in the core than based on the nucleolus, if the gap of the player is no greater than the gap of the complementary coalition. We also investigate the least core value for ADMC games with an empty core. To illustrate the applications of our results, we analyze a code-sharing game, a group buying game, and a scheduling profit game. This paper was accepted by Chung Piaw Teo, optimization.

A cooperative game analysis for the allocation of carbon emissions reduction responsibility in China's power industry

Abstract The allocation of carbon emissions reduction responsibility (CERR) is a fundamental step to carbon emissions trading (CET) market. In China's power industry, regions with divergent power generation efficiencies and energy structures are connected by a nationwide power grid, causing shifts in carbon emissions. We construct a graph restricted cooperative game model for the allocation of CERRs among regions by proposing a novel characteristic function to describe possible minimal carbon emissions in which power generation is prioritized by efficiency. We employ the Myerson value as the solution of the game to capture the structure of the power grid and the power transmission. Our results indicate the following: (1) Power producing regions with high ratio of clean energy such as “Southwest” and “Sichuan and Chongqing” obtain negative shares of CERR. This provides an incentive for them to contribute to carbon emissions reduction. (2) Large power consumers such as “East” and “Bohai Rim” should take larger CERRs because they transfer carbon emissions to the power producing regions. (3) The role of a region in the power transmission network is an important factor in allocating CERR. This study provides insightful policy implications for the construction of a CET market in China's power industry.

Evolutionary game analysis of cooperation between natural resource- and energy-intensive companies in reverse logistics operations

Reverse logistics (RL) plays a significant role in circular economic development, especially in natural resource- and energy-intensive industries (NREI) as a long-term strategy to make a breakthrough in their development. In this study, we construct an evolutionary game theoretical model to investigate the cooperation between NREI companies that adopt one of two reverse logistics operating strategies: self-operation or joint venture. We derive the evolutionary stable strategy of the game through a replicator dynamic system. Simulation experiments are also conducted to validate the theoretical results, to show the evolution, and to analyze the sensitivities to parameters, based on the data of the steel industry that we collected from China. Among many other outcomes, our results show that self-operation is more likely to succeed in operating the current reverse logistics system. The methodologies and results are useful in supporting NREI's reverse logistics decisions. The practical applications of the study can be extended to other NREI sectors when the way of RL implementation is to be decided.