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.

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.

scholarly journals Collusive Behavior of Bidders in English Auctions: A Cooperative Game Theoretic Analysis

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Takayuki Oishi
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Theoretic Analysis ◽  
Single Object ◽  
English Auctions ◽  
Game Theoretic Analysis ◽  
The Core ◽  
Game Theoretic

In practice, collusive bidders' rings in English auctions with a single object frequently distribute collusive gains among ring members via sequences of re-auctions called knockouts. The present paper introduces a model of sequences of knockouts under the situation in which each bidder has information on his evaluation and the order of the evaluations of all bidders for the object. The present paper examines the distributive function of sequences of knockouts from the viewpoint of cooperative game theory. Each sequence of knockouts yields an element of the core, two particular sequences yielding the Shapley value and the nucleolus respectively. The present paper highlights the sequence of knockouts yielding the nucleolus.

scholarly journals Cooperative Game Theory and its Insurance Applications

1991 ◽  
Vol 21 (1) ◽  
pp. 17-40 ◽  
Author(s):  
Jean Lemaire
Keyword(s):  
Game Theory ◽  
Characteristic Function ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Elementary Level ◽  
Stable Sets ◽  
Survey Paper ◽  
The Core ◽  
Basic Concepts

AbstractThis survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five examples, including three insurance applications, are progressively developed throughout the paper. The characteristic function, the core, the stable sets, the Shapley value, the Nash and Kalai-Smorodinsky solutions are defined and computed for the different examples.

scholarly journals The Shapley Value of Tuples in Query Answering

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Approximation Algorithms ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Wealth Distribution ◽  
Coalition Game ◽  
The Shapley Value ◽  
Query Answer ◽  
Aggregate Queries

We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for assessing the contribution of a player to a coalition game. It has been established already in the 1950s, and is theoretically justified by being the very single wealth-distribution measure that satisfies some natural axioms. While this value has been investigated in several areas, it received little attention in data management. We study this measure in the context of conjunctive and aggregate queries by defining corresponding coalition games. We provide algorithmic and complexity-theoretic results on the computation of Shapley-based contributions to query answers; and for the hard cases we present approximation algorithms.

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)

A New Collaborative Filtering Approach Based on Game Theory for Recommendation Systems

2021 ◽  
Author(s):  
Selma Benkessirat ◽  
Narhimene Boustia ◽  
Rezoug Nachida
Keyword(s):  
Game Theory ◽  
Collaborative Filtering ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Recommendation Systems ◽  
Internet Users ◽  
User Communities ◽  
The One

Recommendation systems can help internet users to find interesting things that match more with their profile. With the development of the digital age, recommendation systems have become indispensable in our lives. On the one hand, most of recommendation systems of the actual generation are based on Collaborative Filtering (CF) and their effectiveness is proved in several real applications. The main objective of this paper is to improve the recommendations provided by collaborative filtering using clustering. Nevertheless, taking into account the intrinsic relationship between users can enhance the recommendations performances. On the other hand, cooperative game theory techniques such as Shapley Value, take into consideration the intrinsic relationship among users when creating communities. With that in mind, we have used SV for the creation of user communities. Indeed, our proposed algorithm preforms into two steps, the first one consists to generate communities user based on Shapley Value, all taking into account the intrinsic properties between users. It applies in the second step a classical collaborative filtering process on each community to provide the Top-N recommendation. Experimental results show that the proposed approach significantly enhances the recommendation compared to the classical collaborative filtering and k-means based collaborative filtering. The cooperative game theory contributes to the improvement of the clustering based CF process because the quality of the users communities obtained is better.

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.

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