Game theory in regression modeling: A brief review on Shapley Value regression

2021 ◽  
Vol 16 (2) ◽  
pp. 165-168
Author(s):  
Stan Lipovetsky
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Real Life ◽  
Marketing Research ◽  
Decision Makers ◽  
Regression Coefficients ◽  
Value Analysis ◽  
Robust Solution ◽  
Building Models

The work describes developments in the multiple regression performed for building models resistant to multicollinearity, having meaningful robust solution for individual parameters, convenient for interpretation of the results, and good for prediction. A tool from the cooperative game theory, the Shapley Value analysis, have been tried for estimation of regression coefficients and relative usefulness of the predictors in a model. This approach has been checked and successfully applied in various real-life projects in data analysts for commercial companies. It is useful for decision makers in economics, management, marketing research, and any other practical fields.

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.

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.

A Shapley Value Analysis of the Proposed Canadian Constitutional Amendment Scheme

1973 ◽  
Vol 6 (1) ◽  
pp. 140-143 ◽  
Author(s):  
D.R. Miller
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Constitutional Amendment ◽  
Value Analysis ◽  
A Value ◽  
The Shapley Value ◽  
Relative Value ◽  
Individual Player

The interactions of a group of non-identical voting units may be studied by applying the concept of the Shapley value from n-person co-operative game theory. In this theory one assumes that voting units, or players, may form coalitions of various kinds in order to achieve success in the game, and one may assign a “value” to each such coalition based on what it can accomplish against arbitrary coalitions of the remaining players. The relative value of an individual player is calculated by considering how much he brings to each coalition he might join, that is, by how much the value of that coalition increases because of his membership, and summing this figure over all coalitions of which he could be a part.

Shapley Distance and Shapley Index for Some Special Graphs

2020 ◽  
Vol 30 (04) ◽  
pp. 2050012
Author(s):  
Zhendong Gu ◽  
Shuming Zhou ◽  
Jiafei Liu ◽  
Qianru Zhou ◽  
Dajin Wang
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Wiener Index ◽  
Extremal Graphs ◽  
Complete Multipartite Graph ◽  
Kirchhoff Index ◽  
Multipartite Graph ◽  
Complete Multipartite ◽  
The Cost

The Shapley distance in a graph is defined based on Shapley value in cooperative game theory. It is used to measure the cost for a vertex in a graph to access another vertex. In this paper, we establish the Shapley distance between two arbitrary vertices for some special graphs, i.e., path, tree, cycle, complete graph, complete bipartite, and complete multipartite graph. Moreover, based on the Shapley distance, we propose a new index, namely Shapley index, and then compare Shapley index with Wiener index and Kirchhoff index for these special graphs. We also characterize the extremal graphs in which these three indices are equal.

scholarly journals MODIFICATION OF SHAPLEY VALUE AND ITS IMPLEMENTATION IN DECISION MAKING

2017 ◽  
Vol 9 (1) ◽  
pp. 257-272
Author(s):  
Leszek Zaremba ◽  
Cezary S. Zaremba ◽  
Marek Suchenek
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Computer Program ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Point Of View ◽  
Practical Point ◽  
Actual Strength

Abstract The article presents a solution of a problem that is critical from a practical point of view: how to share a higher than usual discount of $10 million among 5 importers. The discount is a result of forming a coalition by 5 current, formerly competing, importers. The use of Shapley value as a concept for co-operative games yielded a solution that was satisfactory for 4 lesser importers and not satisfactory for the biggest importer. Appropriate modification of Shapley value presented in this article allowed to identify appropriate distribution of the saved purchase amount, which according to each player accurately reflects their actual strength and position on the importer market. A computer program was used in order to make appropriate calculations for 325 permutations of all possible coalitions. In the last chapter of this paper, we recognize the lasting contributions of Lloyd Shapley to the cooperative game theory, commemorating his recent (March 12, 2016) descent from this world.

scholarly journals Modeling the relationship between network operators and venue owners in public Wi-Fi deployment using non-cooperative game theory

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jonathan Spruytte ◽  
Amal Benhamiche ◽  
Matthieu Chardy ◽  
Sofie Verbrugge ◽  
Didier Colle
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Cooperative Game Theory ◽  
Real Life ◽  
Optimal Solution ◽  
Mobile Network ◽  
Data Traffic ◽  
Pricing Models ◽  
Revenue Models ◽  
Roll Out

Abstract Wireless data demands keep rising at a fast rate. In 2016, Cisco measured a global mobile data traffic volume of 7.2 Exabytes per month and projected a growth to 49 Exabytes per month in 2021. Wi-Fi plays an important role in this as well. Up to 60% of the total mobile traffic was off-loaded via Wi-Fi (and femtocells) in 2016. This is further expected to increase to 63% in 2021. In this publication, we look into the roll-out of public Wi-Fi networks, public meaning in a public or semi-public place (pubs, restaurants, sport stadiums, etc.). More concretely we look into the collaboration between two parties, a technical party and a venue owner, for the roll-out of a new Wi-Fi network. The technical party is interested in reducing load on its mobile network and generating additional direct revenues, while the venue owner wants to improve the attractiveness of the venue and consequentially generate additional indirect revenues. Three Wi-Fi pricing models are considered: entirely free, slow access with ads or fast access via paid access (freemium), and paid access only (premium). The technical party prefers a premium model with high direct revenues, the venue owner a free/freemium model which is attractive to its customers, meaning both parties have conflicting interests. This conflict has been modeled using non-cooperative game theory incorporating detailed cost and revenue models for all three Wi-Fi pricing models. The initial outcome of the game is a premium Wi-Fi network, which is not the optimal solution from an outsider’s perspective as a freemium network yields highest total payoffs. By introducing an additional compensation scheme which corresponds with negotiation in real life, the outcome of the game is steered toward a freemium solution.

scholarly journals ON COOPERATIVE GAME APPROACH TO PROFIT SHARING IN A FEW PROJECTS MANAGEMENT PROBLEM

2019 ◽  
pp. 15-22
Author(s):  
N. Boyko ◽  
S. Dotsenko
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Profit Sharing ◽  
Management Problem ◽  
Profit Distribution ◽  
Common Resource

The article is consider three different mechanisms of project’s profit sharing, assuming that the projects have common resource pool and both resources and profit may be distributed at arbitrary way without losses. The resources and profit distribution mechanisms are based on cooperative game theory thesis. As three different alternatives, such cooperative game solutions, as Shapley value, nucleolus ant τ-value are proposed. The calculation routine is delivered by easy typical example.

UNIONS AND UNEMPLOYMENT BENEFITS: SOME INSIGHTS FROM A SIMPLE THREE-PLAYER EXAMPLE

2011 ◽  
Vol 13 (04) ◽  
pp. 383-402
Author(s):  
HARALD WIESE
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Theory Building ◽  
Unemployment Benefits ◽  
Tu Games ◽  
Coalition Structures ◽  
A Value ◽  
Basic Input

The aim of this paper is to analyze the interconnections between employment and unionization. We will also see how unemployment benefits drive the interplay of employment and unionization. The basic input into our model stems from cooperative game theory. Building on the Shapley value, several values for TU games with coalition structures have been presented in the literature, most notably by Aumann and Drèze and Owen. We present a value that is capable of dealing with unemployment and unionization. We show that unemployment benefits increase wages but contribute to unemployment, that unemployment can be voluntary, and that unions tend to be beneficial for employed workers if there is overstaffing.

scholarly journals Blameworthiness in Multi-Agent Settings

2019 ◽  
Vol 33 ◽  
pp. 525-532 ◽  
Author(s):  
Meir Friedenberg ◽  
Joseph Y. Halpern
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Autonomous Agents ◽  
Cooperative Game Theory ◽  
Epistemic State ◽  
Formal Definition ◽  
Group Setting ◽  
Standard Notion ◽  
Multi Agent ◽  
Definition Of

We provide a formal definition of blameworthiness in settings where multiple agents can collaborate to avoid a negative outcome. We first provide a method for ascribing blameworthiness to groups relative to an epistemic state (a distribution over causal models that describe how the outcome might arise). We then show how we can go from an ascription of blameworthiness for groups to an ascription of blameworthiness for individuals using a standard notion from cooperative game theory, the Shapley value. We believe that getting a good notion of blameworthiness in a group setting will be critical for designing autonomous agents that behave in a moral manner.

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.

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