Cooperative games with additive multiple attributes

2021 ◽  
Vol 41 (1) ◽  
pp. 1135-1150
Author(s):  
Haitao Liu ◽  
Qiang Zhang
Keyword(s):  
Finite Number ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Games ◽  
Polynomial Form ◽  
The Core ◽  
The Shapley Value ◽  
Efficient Resource ◽  
Multiple Attributes ◽  
Special Case

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.

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.

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

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

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.

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.

APPLICATIONS OF GAME THEORY TO ECONOMICS

2013 ◽  
Vol 15 (03) ◽  
pp. 1340011 ◽  
Author(s):  
GUILLERMO OWEN
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Core ◽  
The Shapley Value

We look at the basic applications of cooperative game theory to economic situations. These include bargaining and cooperative equilibria, especially as the number of players increases without bound. The core and the Shapley value are the fundamental tools for these applications. We consider the relation between these two concepts. A comprehensive bibliography of work published over the last decade is included.

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)

scholarly journals Cooperative optimality principals in differential games on networks

2020 ◽  
Vol 12 (4) ◽  
pp. 93-111
Author(s):  
Анна Тур ◽  
Anna Tur ◽  
Леон Аганесович Петросян ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
The Core ◽  
Investment Game ◽  
The Shapley Value ◽  
Research Investment ◽  
Optimality Principles

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.

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