Attaining Fairness in Communication for Omniscience

This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by their remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed which utilizes the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed that converges in polynomial time on the fractional egalitarian solution in the core, which can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity.

Mathematical indices for the influence of risk factors on the lethality of a disease

We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19.

Shapley-Based Estimation of Company Value—Concept, Algorithms and Parameters

The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson’s correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies.

Penentuan Strategi Pemasaran dari Penjualan Air Minum Dalam Kemasan Lokal dan Nasional Menggunakan Metode Fuzzy Shapley Value

Air minum dalam kemasan (AMDK) adalah air baku yang telah melalui sebuah proses sterilisasi, dikemas, dan aman untuk diminum mencakup air mineral dan air demineral. Beberapa tahun terakhir ini penjualan AMDK di Indonesia berkembang sangat pesat sehingga perlu diadakannya penentuan strategi pemasaran dari penjualan AMDK lokal dan nasional. Penjualan merupakan salah satu indikator paling penting dalam sebuah perusahaan, bila tingkat penjualan yang dihasilkan oleh perusahaan tersebut besar, maka laba yang dihasilkan perusahaan itupun akan besar pula, sehingga perusahaan dapat bertahan dalam persaingan bisnis dan bisa mengembangkan usahanya baik itu AMDK lokal ataupun nasional. Metode yang dapat digunakan dalam penentuan strategi pemasaran AMDK lokal dan nasional adalah metode fuzzy Shapley Value. Dan dari hasil penerapan metode Fuzzy Shapley Value dengan menggunakan persentase penjualan adalah 25%, desain 32% dan harga 43%, harga memiliki nilai fuzzy shapley value terbesar dalam menentukan strategi pemasaran dari penjualan air minum dalam kemasan lokal ataupun nasional. Jadi, hasil harga ini dapat dijadikan pedoman strategi pemasaran dalam memberikan penilaian terhadap produk air minum dalam kemasan lokal dan nasional.

Conceptual Solution Decision Based on Rough Sets and Shapley Value for Product-Service System: Customer Value-Economic Objective Trade-Off Perspective

The product service system (PSS), as a design concept for integrated products and services, needs to be evaluated in the early design stage to maximize the value for stakeholders of the PSS concept, which is a crucial task for enterprises. However, existing methods focus on the ranking and value assessment of PSS evaluation criteria (e.g., quality, sustainability, cost), ignoring the needs conflict between customer value and economic objectives in PSS design, resulting in decision results that are not applicable to industrial enterprises. Furthermore, the influence of weight preference and uncertain information on solution evaluation is seldom considered when calculating the weight of each criterion. To fill this gap, integrating rough sets and the Shapley value decision approach for product-service system design considering customer value-economic objective trade-off is proposed, which mainly includes two parts: firstly, the best worst method (BWM) and the entropy weight method are integrated to obtain the comprehensive weight of evaluation criteria in the customer value and economic objectives; secondly, the Shapley value method in the coalition game is used to solve the optimal expectation allocation of the two objectives, so as to select the solution closest to the allocation, i.e., the optimal solution. In addition, rough set techniques are used to capture and integrate subjective assessment information originating from DMs under uncertainty. Finally, a case study of the electric forklift design is illustrated to verify the proposed decision model. The decision results show that this approach is more reliable through sensitivity and comparison analysis, and provide a valuable recommendation for enterprises to consider product service in forklift design.

Redistribution of tax resources: a cooperative game theory approach

We consider the problem of how to distribute public expenditure among the different regions of an economic entity after all taxes have been collected. Typical examples are: the regions that make up a country, the states of a federal country, or the countries of a confederation of countries. We model the problem as a cooperative game in coalitional form, called the tax game. This game estimates the fiscal resources collected in each region, or coalition of regions, by differentiating between what comes from economic activity within each region and what comes from trade with the other regions. This methodology provides a measure of the disagreement within a region, or coalitions of regions, with respect to the budget received. Similarly, the stability of a budget allocation can be inferred by its situation within the core of the corresponding tax game. We consider the Spanish case as an example and show that the current regional financial system has a moderate degree of instability. We introduce two budget allocation rules, both borrowed from the cooperative games literature: the balanced allocation, which coincides with the nucleolus and with the Shapley value of the tax game, and the weighted balanced allocation, which coincides with the weighted Shapley value. We compare both budget allocation rules with the current Spanish financial system.

Shapley value cooperative game theory-based locational marginal price computation for loss and emission reduction

An iterative method based on Shapley Value Cooperative Game Theory is proposed for the calculation of local marginal price (LMP) for each Distributed Generator (DG) bus on a network. The LMP value is determined for each DG on the basis of its contribution to reduce loss and emission reduction, which is assessed using the Shapley Value approach. The proposed approach enables the Distribution Company (DISCO) decision-maker to operate the network optimally in terms of loss and emission. The proposed method is implemented in the Taiwan Power Company distribution network 7 warnings consisting of 84 buses and 11 feeders in the MATLAB environment. The results show that the proposed approach allows DISCO to operate the network on the basis of its priority between the reduction of active power loss and emission in the network