Solutions For Cooperative Games Research Articles

Updated delegated proof of stake and Nash equilibrium: A mining pool game model for blockchain network

SummaryIn the present era, blockchain technology has an extensive variety of uses in the financial, marketing, and so forth. The performance and security of the blockchain system are directly affected by the consensus algorithm. Since there are 30 consensus techniques like proof of stake, delegated proof of stake, and proof of work, and so forth in the previous years, the operating efficiency, safety, and stability still lag behind the basic requirements. To this concern, this research manuscript introduces a novel consensus mechanism‐based game model using upgraded delegated proof of stake (UDPoS) and Nash equilibrium (NE) that is UDPoS‐NE. In a blockchain network powered by UDPoS, blockchain miners provide computing power to publish blocks. Due to a single miner's limited Computing Power (CP), miners frequently join mining pools and divide the pool's profits in accordance with their respective contributions. However, certain miners launch block‐withholding attacks that lead to loss the computer power and endanger the blockchain network's effectiveness. Therefore, NE is used to calculate cooperative game solutions and optimize policy decisions of the miners to frustrate the block withholding attack by the influence of stakes and computing power on producing blocks. Using this mechanism, efficiency, and stability in the consensus process is achieved through the combined influence of computing resources and stakes on block generation. Finally, the suggested model's applicability and validity are confirmed with a throughput (600 TPS), delay (3 s), and energy consumption (<100 KWh) for 10 nodes and processing time (0.9 s) for 200 nodes.

Collaborative game-based task offloading scheme in the UAV-TB-assisted battlefield network platform

In the sixth-generation (6G) wireless networks, the use of unmanned aerial vehicles (UAVs) and tethered balloons (TBs) to assist cellular networks has attracted considerable attentions due to their dynamic and quick deployment with their relative low cost. In this article, we propose a new task offloading scheme for smart devices in the modern battlefield area. By the integrative platform of TBs, UAVs and smart devices, the main challenges are (i) providing a task splitting algorithm for the partial offloading service, and (ii) develop a TB resource sharing algorithm to handle the offloading requests. For convenient wireless communications, UAVs work as relay nodes between TBs and individual devices. To achieve a mutually desirable solution, our proposed scheme is formulated as cooperative game models. First, the sequential Raiffa bargaining solution is applied to split the computation-intensive task of each smart device in the battlefield area. Second, the average-surplus value is adopted to effectively share the TB computing resource. Based on the reciprocal combination of two cooperative game solutions, we explore the sequential interaction of TBs, UAVs and battlefield devices, and jointly design our integrated control scheme for offloading services. According to the synergy effect, our hybrid approach can provide a fair-efficient solution in the UAV-TB-assisted battlefield network infrastructure. Finally, extensive simulations are conducted, and the results demonstrate the superiority of our proposed scheme over the existing baseline protocols.

Modeling Norm-Governed Communities with Conditional Games: Sociological Game-Determination and Economic Equilibria

Most social scientists agree that informal norms constrain available equilibria in most human interactions. However, they do not agree on how to model them: economists often make them derivative of individual preferences, while a broader tradition in social theory understands them as exogenous social facts. Non-cooperative game theory more naturally accommodates the economists’ approach. However, attention is increasingly attracted to recent work by economists who appreciate that the broader understanding may be important for full empirical adequacy. We focus on how game theorists might track this emerging shift. Extending Stirling’s previously developed Conditional Game Theory, we model macrostructural processes of norm evolution through social influence diffusion in a way that relies on no exotic solution concepts, which in turn allows norms as social facts and norms as expressions of preferences to be modeled as evaluable complements, by analogy to the complementarity of cooperative and non-cooperative game solutions under the Nash program. The result can be understood as a way of specifying mutual constraints between economic models in which normative attitudes are exogenous, and sociological models that represent such attitudes as endogenous under power relationships and ontologies of social roles.

Potentials and solutions of cooperative games with a fixed player set

Potentials and solutions of cooperative games with a fixed player set

On the structure of core solutions of discontinuous general cooperative games

On the structure of core solutions of discontinuous general cooperative games

Players’ dummification and the dummified egalitarian non-separable contribution value

This paper introduces a new solution for cooperative games, called dummified egalitarian non-separable contribution (DENSC) value. This value is obtained by minimizing the variance of so-called dummified grand complaints of coalitions, and is characterized in term of the axioms on players’ dummification.

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

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

Two-Phase Wireless Bandwidth Allocation Scheme Based on Cooperative Game Solutions

Two-Phase Wireless Bandwidth Allocation Scheme Based on Cooperative Game Solutions

Cooperative game theory approach to develop an incentive mechanism for biopesticide adoption through farmer producer organizations

Biopesticides have been recognized as viable alternatives to chemical pesticides in controlling agricultural pests for plants and reducing harmful chemical residues. However, small and marginal farmers are facing challenges while adopting biopesticides, namely, high cost and complicated application techniques, resulting in a low level of farmer acceptance. Accordingly, Farmer Producer Organizations (FPOs), voluntarily formed by farmers, develop mutual technical assistance among their members to solve the technical problems of biopesticide adoption. This study assumes that as a new form of farmer cooperative, FPOs have the potential to promote biopesticide adoption through the implementation of collective pesticide adoption (CPA). Along this line, this paper uses a cooperative game-based hybrid method to develop an incentive mechanism of biopesticide adoption for FPOs to implement CPAs. First, we construct a CPA decision model for mixed pesticides (i.e., biopesticides and chemical pesticides) based on multichoice goal programming (MCGP) to compromise the conflicting objectives regarding cost efficiency and chemical residue reduction, thereby obtaining the optimal total cost of pesticide adoption. Second, recognizing the optimal total adoption cost as a baseline, we devise a cooperative game-based cost allocation scheme to maintain farmers' voluntary participation in FPOs. This study demonstrates that the CPA implemented based on our proposed models can at least match if not surpass the economic and environmental performance of farmers' independent pesticide adoption (IPA). We further demonstrate that the proposed cooperative game solution is more suitable for the FPO's cost allocation issue than the eminent solutions, such as the Shapley value.

Cooperative solutions for TU and NTU stochastic game-theoretical approach

The player's payoff in stochastic games is a stochastic variable. In most studies, predicted payout is referred to as a payoff, implying that the players are risk averse. However, there may be risk-averse players that consider "risk" while calculating their stochastic payoffs. We offer a model of stochastic games using mean-variance reward functions, which are the sum of expectation and standard deviation multiplied by a coefficient indicating a player's risk aversion. By adopting a maxmin technique to define the characteristic function, we may create a cooperative version of a stochastic game with mean-variance preferences. This paper contains an analysis of a cooperative solution concept of stochastic games for both TU (transferable utility) and NTU (non-transferable utility) games. We proposed a cooperative game solution method of extension of two-person zero sum strategic game to n-agent stochastic stage game using both Shapley and Banzhaf index functions. Results are proved for both discounted and undiscounted payoff situations. Existing models of discrete-time stochastic games and ways to finding cooperative solutions in these games are extended in this study.

Nonadditive Integration and Some Solutions of Cooperative Games

Nonadditive Integration and Some Solutions of Cooperative Games

Collaborative Resource Sharing Game Based Cloud-Edge Offload Computing Orchestration Scheme

In the foreseeable future, the rapid growth of mobile communications and cloud systems has substantially promoted edge computing paradigm. Although edge computing technology has been attracting much interest, most current research is application-specific without considering a control perspective of cloud providers that provides general-purpose edge services. In this study, we present a new cloud-edge computing orchestration scheme that integrates the different resource sharing problems to maximize benefits for offloading computing services. Specifically, we focus on two cooperative game solutions - <i>Sim bargaining solution</i> and <i>interval Banzhaf Value</i> - to effectively share the computing, communication and cache resources in the cloud-edge system platform. In the proposed scheme, we formalize two different cooperative games, and they work together and act cooperatively to satisfy contradictory requirements. Under widely different service request situations, we aim at accelerating an efficient resource orchestration through dynamic workload balancing. The primary goal of our cooperative game approach is to find optimal control decisions toward the appropriate system operation. Finally, we evaluate the proposed scheme in terms of several performance criteria from the numerical simulations. Experimental results show that we can achieve a mutually desirable solution with a good system performance balance while enhancing the resource efficiency better than the existing cloud-edge control protocols.

Potentials and Solutions of Cooperative Games

This paper considers the solution concepts of cooperative games that admit a potential function. We say that a solution admits a potential function if the solution is given as the gradient vector of the potential function at the player set. Hart and Mas-Collel (1989) show that the Shapley value is the only solution that is efficient and admits the potential function for games with variable player sets. In this paper, first, we argue that if we remove efficiency, various solutions admit a potential function. Second, we characterize the class of the solutions that admit a potential function and provide their general functional form. Third, we define a potential function for games with a fixed player set and associate a potential function with the axioms that the Shapley value obeys. Finally, we discuss how the efficiency requirement induces the uniqueness of the Shapley value through a potential function.

Matrix expression of Owen values

AbstractThe Owen value is investigated in this paper. It is a generation of Shapley value as a solution of cooperative games with coalition structures. First, a characteristic function of a cooperative game is expressed as a pseudo‐logical function by using semi‐tensor product of matrices. Then, a matrix formula is given for calculating Owen values. The matrix formula not only makes computing more convenient but also facilitates theoretical analysis. Therefore, an application of Owen value in distributed welfare games is presented. Utility functions of a distributed welfare game with coalition structure are designed based on Owen value. Examples are showed to illustrate the theoretical results.

Hart–Mas-Colell consistency and the core in convex games

This paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

Cooperative games with additive multiple attributes

This paper studies cooperative games in which players have multiple attributes. Such games are applicable to situations in which each player has a finite number of independent additive attributes in cooperative games and the payoffs of coalitions are endogenous functions of these attributes. The additive attributes cooperative game, which is a special case of the multiattribute cooperative game, is studied with respect to the core, the conditions for existence and boundedness and methods of transformation regarding a general cooperative game. A coalitional polynomial form is also proposed to discuss the structure of coalition. Moreover, a Shapley-like solution called the efficient resource (ER) solution for additive attributes cooperative games is studied via the axiomatical method, and the ER solution of two additive attribute games with equivalent total resources coincides with the Shapley value. Finally, some examples of additive attribute games are given.

On the fuzzy interval equal surplus sharing solutions

PurposeThis paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means that one observes a lower and an upper bound of the considered coalitions. This is very important, for example, from a computational and algorithmic viewpoint. The authors notice that the approach is general, since the characteristic function fuzzy interval values may result from solving general optimization problems.Design/methodology/approachThis paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. A situation in which a finite set of players can obtain certain fuzzy payoffs by cooperation can be described by a cooperative fuzzy interval game.FindingsIn this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty.Originality/valueIn this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty. Examples of such solutions are the centre-of-gravity of the imputation-set value, shortly denoted by CIS value, egalitarian non-separable contribution value, shortly denoted by ENSC value and the equal division solution. Further, the authors discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS value, the ENSC value and the equal division solution. The authors provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.

A cooperative game solution approach for intensity modulated radiation therapy design: Nash Social Welfare optimization

We study the fluency map optimization problem in Intensity Modulated Radiation Therapy from a cooperative game theory point of view. We consider the cancerous and healthy organs in a patient’s body as players of a game, where cancerous organs seek to eliminate the cancerous cells and healthy organs seek to receive no harm. The goal is to balance the trade-offs between the utility of players by forming a grand coalition between them. We do so by proposing a methodology that solves a few convex optimization problems in order to transform the fluency map optimization problem into a bargaining game. To solve the bargaining game, we employ the concept of Nash Social Welfare (NSW) optimization due to the desirable efficiency and fairness properties of its outcomes. The proposed NSW optimization is convex and can be solved by powerful commercial solvers such as CPLEX. An additional advantage of the proposed approach is that it has a new control lever for the fluency map optimization, the so-called negotiation powers, which enables practitioners to put more emphasis on an organ by changing its negotiation power. To show the efficacy of our proposed methodology, we apply it to the TG-119 case and a liver case. We compare our proposed approach with a state-of-the-art approach through creating Dose Volume Histograms.

Nonadditive integration and some solutions of cooperative games

In the paper, we propose three schemes of nonadditive integration based on several extensions of nonadditive set function and integrand to the appropriate symmetric power of the original measurable space. A survey on the integral representation of some classic objects of the cooperative game theory, derived by nonadditive integration, is given. A universal approach for investigation of both finite and infinite games is developed. We pay a particular attention to the Shapley value, Owen multilinear extension, and support function of the core of a convex cooperative game.

A dynamic transfer scheme deriving from the dual similar associated game

Dynamic process is an approach to cooperative games, and it can be defined as that which leads the players to a solution for cooperative games. Hwang et al. (2005) adopted Hamiache’s associated game (2001) to provide a dynamic process leading to the Shapley value. In this paper, we propose a dynamic transfer scheme on the basis of the dual similar associated game, to lead to any solution satisfying both the inessential game property and continuity, starting from an arbitrary efficient payoff vector.