scholarly journals Allocation of Environmental Impacts in Circular and Cascade Use of Resources—Incentive-Driven Allocation as a Prerequisite for Cascade Persistence

2020 ◽  
Vol 12 (11) ◽  
pp. 4366
Author(s):  
Max Rehberger ◽  
Michael Hiete

In cascade use, a resource is used consecutively in different application areas demanding less and less quality. As this practically allows using the same resource several times, cascading contributes to resource efficiency and a circular economy and, therefore, has gained interest recently. To assess the advantages of cascading and to distribute the environmental impacts arising from resource extraction/processing, potentially needed treatment and upcycling within the cascade chain and end-of-life proesses represent a difficult task within life cycle assessment and highlight the needs for a widely applicable and acceptable framework of how to allocate the impacts. To get insight into how the allocation is handled in cascades, a systematic literature review was carried out. Starting from this status quo, common allocation approaches were extracted, harmonized, and evaluated for which a generic set of criteria was deduced from the literature. Most importantly, participants must be willing to set up a cascade, which requires that for each participant, there are individual benefits, e.g., getting less environmental burdens allocated than if not joining. A game-theoretic approach based on the concept of the core and the Shapley value was presented, and the approaches were benchmarked against this in a case-study setting. Several of the approaches laid outside the core, i.e., they did not give an incentive to the participants to join the cascade in the case study. Their application for cascade use is, therefore, debatable. The core was identified as an approach for identifying suitable allocation procedures for a problem at hand, and the Shapley value identified as a slightly more complex but fair allocation procedure.

2020 ◽  
Vol 12 (4) ◽  
pp. 93-111
Author(s):  
Анна Тур ◽  
Anna Tur ◽  
Леон Аганесович Петросян ◽  
Leon Petrosyan

The paper describes a class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. The core, the Shapley value and the tau-value are used as cooperative optimality principles. The results are demonstrated on a model of a differential research investment game, where the Shapley value and the tau-value are explicitly constructed.


2018 ◽  
Vol 63 ◽  
pp. 145-189 ◽  
Author(s):  
Mateusz K. Tarkowski ◽  
Piotr L. Szczepański ◽  
Tomasz P. Michalak ◽  
Paul Harrenstein ◽  
Michael Wooldridge

Some game-theoretic solution concepts such as the Shapley value and the Banzhaf index have recently gained popularity as measures of node centrality in networks. While this direction of research is promising, the computational problems that surround it are challenging and have largely been left open. To date there are only a few positive results in the literature, which show that some game-theoretic extensions of degree-, closeness- and betweenness-centrality measures are computable in polynomial time, i.e., without the need to enumerate the exponential number of all possible coalitions. In this article, we show that these results can be extended to a much larger class of centrality measures that are based on a family of solution concepts known as semivalues. The family of semivalues includes, among others, the Shapley value and the Banzhaf index. To this end, we present a generic framework for defining game-theoretic network centralities and prove that all centrality measures that can be expressed in this framework are computable in polynomial time. Using our framework, we present a number of new and polynomial-time computable game-theoretic centrality measures.


Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter

AbstractThis 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.


2019 ◽  
Vol 7 (1) ◽  
pp. 1-16
Author(s):  
Cui Liu ◽  
Hongwei Gao ◽  
Ovanes Petrosian ◽  
Juan Xue ◽  
Lei Wang

Abstract Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.


2020 ◽  
Vol 1 (2) ◽  
pp. 1-5
Author(s):  
Rahul Lakhotia ◽  
Pratibha Goenka

Market Basket Analysis is an interesting concept wherein a set of historical purchase data is studied extensively and data-mining techniques are applied to predict a user’s purchase behavior. In the resent times, every e-commerce giant, like Amazon, Flip-kart etc. are trying to increase their sales by this technique. It has been found in study that when a user is purchasing an item then he/she might be interested in purchasing other items too. So, by analyzing this purchase behavior if we can recommend other products at the time of purchasing then that could increase the sale and profit as well. Analyzing the correlation among the products by studying the purchase pattern and then finding the associated products is the main objective of Market Basket Analysis. Several algorithms have been developed to find the association among the products. But most of the traditional algorithms are based on support value of the product. They do not consider another important factor i.e. the marginal contribution of the product. Considering this into account in this paper we are going to propose a Shapley Value based game theoretic approach for market basket analysis. Shapley Value is a well-known solution concept in cooperative game theory. It gives the measure of marginal contribution of a player in a cooperative game.


2020 ◽  
Author(s):  
Mingming Leng ◽  
Chunlin Luo ◽  
Liping Liang

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.


2021 ◽  
Author(s):  
Roma Patel ◽  
Marta Garnelo ◽  
Ian Gemp ◽  
Chris Dyer ◽  
Yoram Bachrach

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