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

2021 ◽  
Vol 83 (6-7) ◽  
Author(s):  
Ricardo Martínez ◽  
Joaquín Sánchez-Soriano
Keyword(s):  
Risk Factors ◽  
Theoretical Model ◽  
Cooperative Game ◽  
Shapley Value ◽  
The Other ◽  
Prevention Strategies ◽  
The Shapley Value ◽  
Vaccination Campaigns

AbstractWe 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.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions

2019 ◽  
Vol 7 (1) ◽  
pp. 1-16
Author(s):  
Cui Liu ◽  
Hongwei Gao ◽  
Ovanes Petrosian ◽  
Juan Xue ◽  
Lei Wang
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
The Core ◽  
The Shapley Value ◽  
Irrational Behavior ◽  
The Individual

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.

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

2020 ◽  
Author(s):  
Mingming Leng ◽  
Chunlin Luo ◽  
Liping Liang
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Extreme Points ◽  
Game Analysis ◽  
The Core ◽  
The Shapley Value ◽  
Code Sharing ◽  
Marginal Contributions ◽  
Least Core ◽  
Necessary And Sufficient

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.

scholarly journals Early Life Microbial Exposure and Immunity Training Effects on Asthma Development and Progression

2021 ◽  
Vol 8 ◽  
Author(s):  
Andressa Daronco Cereta ◽  
Vinícius Rosa Oliveira ◽  
Ivan Peres Costa ◽  
Letícia Lopes Guimarães ◽  
João Pedro Ribeiro Afonso ◽  
...  
Keyword(s):  
Risk Factors ◽  
Early Life ◽  
Inflammatory Diseases ◽  
Adult Life ◽  
Allergic Diseases ◽  
Postnatal Period ◽  
The Other ◽  
Prevention Strategies ◽  
New Ideas ◽  
Lung Immunity

Asthma is the most common inflammatory disease affecting the lungs, which can be caused by intrauterine or postnatal insults depending on the exposure to environmental factors. During early life, the exposure to different risk factors can influence the microbiome leading to undesired changes to the immune system. The modulations of the immunity, caused by dysbiosis during development, can increase the susceptibility to allergic diseases. On the other hand, immune training approaches during pregnancy can prevent allergic inflammatory diseases of the airways. In this review, we focus on evidence of risk factors in early life that can alter the development of lung immunity associated with dysbiosis, that leads to asthma and affect childhood and adult life. Furthermore, we discuss new ideas for potential prevention strategies that can be applied during pregnancy and postnatal period.

A TWO-STEP SHAPLEY VALUE FOR COOPERATIVE GAMES WITH COALITION STRUCTURES

2009 ◽  
Vol 11 (02) ◽  
pp. 207-214 ◽  
Author(s):  
YOSHIO KAMIJO
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Solution Concept ◽  
The Other ◽  
Value Of A Game ◽  
Coalition Structures ◽  
The Shapley Value ◽  
Original Definition ◽  
Marginal Contributions ◽  
Weighted Shapley Value

In this paper, we study cooperative games with coalition structures. We show that a solution concept that applies the Shapley value to games among and within coalitions and in which the pure surplus that the coalition obtains is allocated among the intra-coalition members in an egalitarian way, is axiomatized by modified axioms on null players and symmetric players and the usual three axioms: efficiency, additivity and coalitional symmetry. In addition to the original definition, we give two expressions of this solution concept. One is an average of modified marginal contributions and the other is the weighted Shapley value of a game with restricted communication.

The Shapley Value for Stochastic Cooperative Game

2008 ◽  
Vol 2 (4) ◽  
Author(s):  
Ying Ma ◽  
Zuofeng Gao ◽  
Wei Li ◽  
Ning Jiang ◽  
Lei Guo
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
The Shapley Value

scholarly journals Convex Interval Games

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
S. Z. Alparslan Gök ◽  
R. Branzei ◽  
S. Tijs
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Allocation Scheme ◽  
Weber Set ◽  
The Shapley Value ◽  
Interval Games

Convex interval games are introduced and characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. The notion of population monotonic interval allocation scheme (pmias) in the interval setting is introduced and it is proved that each element of the Weber set of a convex interval game is extendable to such a pmias. A square operator is introduced which allows us to obtain interval solutions starting from the corresponding classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.

MARKETING DECISION ANALYSIS BY TURF AND SHAPLEY VALUE

2005 ◽  
Vol 04 (01) ◽  
pp. 5-19 ◽  
Author(s):  
W. MICHAEL CONKLIN ◽  
STAN LIPOVETSKY
Keyword(s):  
Game Theory ◽  
Decision Analysis ◽  
Marketing Strategy ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Product Mix ◽  
Marketing Decision ◽  
The Shapley Value ◽  
Sample Proportion

We consider a problem of marketing decisions for the choice of a product with maximum customer appeal. A widely used technique for this purpose is TURF, or Total Unduplicated Reach and Frequency, which evaluates a union of the events defined by the sample proportion of many products, or flavors of one product. However, when using TURF, it is often impossible to distinguish between subsets of different flavor combinations with practically the same level of coverage. An appropriate tool can be borrowed from cooperative game theory, namely, the Shapley Value, that permits the ordering of flavors by their strength in achieving maximum consumers' reach and provides more stable results than TURF. We describe marketing strategy reasons for using these techniques in the identification of the preferred combinations in media or product mix.

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