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- Elsevier B.V. Sa
- Physica-Verlag GMBH & Co
- Universidade Rice
- Universidade Carlos III de Madrid
- Universidad EAFIT
- Universidade Cornell
- Conselho Superior de Investigações Científicas
- Elsevier
- Universidade Autônoma de Barcelona
- Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade
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## A cooperative game theory analysis for transmission loss allocation

Fonte: Elsevier B.V. Sa
Publicador: Elsevier B.V. Sa

Tipo: Artigo de Revista Científica
Formato: 264-275

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This paper presents an analysis and discussion, based on cooperative game theory, for the allocation of the cost of losses to generators and demands in transmission systems. We construct a cooperative game theory model in which the players are represented by equivalent bilateral exchanges and we search for a unique loss allocation solution, the Core. Other solution concepts, such as the Shapley Value, the Bilateral Shapley Value and the Kernel are also explored. Our main objective is to illustrate why is not possible to find an optimal solution for allocating the cost of losses to the users of a network. Results and relevant conclusions are presented for a 4-bus system and a 14-bus system. (c) 2007 Elsevier B.V. All rights reserved.

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## Characterizing the Shapley value in fixed-route traveling salesman problems with appointments

Fonte: Physica-Verlag GMBH & Co
Publicador: Physica-Verlag GMBH & Co

Tipo: Artigo de Revista Científica

Publicado em //2012
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#Fixed-route traveling salesman games#Routing games#Appointment games#The Shapley value#The core#Transferable-utility games#Merging and splitting proofness#Networks#Cost allocation

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to find a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We introduce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We characterize the Shapley value in this class using a property which requires that sponsors do not benefit from mergers, or splitting into a set of sponsors.; Duygu Yengin

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## Energy Accounting and Optimization for Mobile Systems

Fonte: Universidade Rice
Publicador: Universidade Rice

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Energy accounting determines how much a software process contributes
to the total system energy consumption. It is the foundation for
evaluating software and has been widely used by operating system based
energy management. While various energy accounting policies have been
tried, there is no known way to evaluate them directly simply because
it is hard to track every hardware use by software in a heterogeneous
multicore system like modern smartphones and tablets. This work
provides the ground truth for energy accounting based on multi-player
game theory and offers the first evaluation of existing energy
accounting policies, revealing their important flaws. The proposed
ground truth is based on Shapley value, a single value solution to
multi-player games of which four axiomatic properties are natural and
self-evident to energy accounting.
This work further provides a utility optimization formulation of
energy management and shows, surprisingly, that energy accounting does
not matter for existing energy management solutions that control the
energy use of a process by giving it an energy budget, or budget based
energy management (BEM). This work shows an optimal energy management
(OEM) framework can always outperform BEM. While OEM does not require
any form of energy accounting...

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## The Shapley group value

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: Trabalho em Andamento

Publicado em 01/11/2013
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Following the original interpretation of the Shapley value (Shapley, 1953a)
as a priori evaluation of the prospects of a player in a multi-person iteraction situation,
we propose a group value, which we call the Shapley group value, as a priori evaluation
of the prospects of a group of players in a coalitional game when acting as a unit. We
study its properties and we give an axiomatic characterization. We motivate our
proposal by means of some relevant applications of the Shapley group value, when it is
used as an objective function by a decision maker who is trying to identify an optimal
group of agents in a framework in which agents interact and the attained benefit can be
modeled by means of a transferable utility game. As an illustrative example we analyze
the problem of identifying the set of key agents in a terrorist network.; This research has been supported by I+D+i research project MTM2011-27892 from the Government of Spain

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## The value of shapley as a strategy for Resource Optimization on Power Line Communication (PLC); El Valor de Shapley como estrategia de optimizaci??n de recursos sobre Power Line Communication (PLC)

Fonte: Universidad EAFIT
Publicador: Universidad EAFIT

Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; article; Art??culo
Formato: application/pdf; text/html

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#game theory#HPAV#OFDM, Power Line Communication#Shapley#comunicaciones por l??nea de potencia#HPAV#OFDM#Shapley#teor??a de juegos

This article proposes the use of cooperative game theory, supported by the use of bankruptcy game of the and the Shapley value, as a strategy to optimize the allocation of resources in each node, according to service demand, the number of stations and the conditions of the PLC channel. The paper proposes a scenario under saturated traffic conditions, in order to assess the degree of optimization that the value of Shapley can perform in front of traffic and channel conditions clearly established. It is concluded that the use of cooperative game theory, supported on the Shapley value, can be considered as an excellent alternative when making resource optimization processes in a PLC channel y with the possibility to be implemented in economic embedded systems, because it does not require complex operations for its estimation.; En este art??culo se propone el uso de la teor??a de juegos cooperativos, apoyados en el uso del juego de la bancarrota y el valor de Shapley, como estrategia para optimizar la asignaci??n de recursos en cada nodo, acorde con la demanda en el servicio, el n??mero de estaciones y las condiciones del canal PLC. El art??culo plantea un escenario bajo condiciones de tr??fico saturado, con el fin de evaluar el grado de optimizaci??n que el valor de Shapley puede realizar ante condiciones de tr??fico y de canal claramente establecidas. Se concluye que el uso de la teor??a juegos cooperativos...

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## Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/02/2014
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The Shapley value---probably the most important normative payoff division
scheme in coalitional games---has recently been advocated as a useful measure
of centrality in networks. However, although this approach has a variety of
real-world applications (including social and organisational networks,
biological networks and communication networks), its computational properties
have not been widely studied. To date, the only practicable approach to compute
Shapley value-based centrality has been via Monte Carlo simulations which are
computationally expensive and not guaranteed to give an exact answer. Against
this background, this paper presents the first study of the computational
aspects of the Shapley value for network centralities. Specifically, we develop
exact analytical formulae for Shapley value-based centrality in both weighted
and unweighted networks and develop efficient (polynomial time) and exact
algorithms based on them. We empirically evaluate these algorithms on two
real-life examples (an infrastructure network representing the topology of the
Western States Power Grid and a collaboration network from the field of
astrophysics) and demonstrate that they deliver significant speedups over the
Monte Carlo approach. For instance...

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## Steady Marginality: A Uniform Approach to Shapley Value for Games with Externalities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/05/2011
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The Shapley value is one of the most important solution concepts in
cooperative game theory. In coalitional games without externalities, it allows
to compute a unique payoff division that meets certain desirable fairness
axioms. However, in many realistic applications where externalities are
present, Shapley's axioms fail to indicate such a unique division.
Consequently, there are many extensions of Shapley value to the environment
with externalities proposed in the literature built upon additional axioms. Two
important such extensions are "externality-free" value by Pham Do and Norde and
value that "absorbed all externalities" by McQuillin. They are good reference
points in a space of potential payoff divisions for coalitional games with
externalities as they limit the space at two opposite extremes. In a recent,
important publication, De Clippel and Serrano presented a marginality-based
axiomatization of the value by Pham Do Norde. In this paper, we propose a dual
approach to marginality which allows us to derive the value of McQuillin. Thus,
we close the picture outlined by De Clippel and Serrano.

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## The Shapley Value of Phylogenetic Trees

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Quantitative Biology - Quantitative Methods#Computer Science - Computer Science and Game Theory#Mathematics - Combinatorics#Quantitative Biology - Populations and Evolution

Every weighted tree corresponds naturally to a cooperative game that we call
a "tree game"; it assigns to each subset of leaves the sum of the weights of
the minimal subtree spanned by those leaves. In the context of phylogenetic
trees, the leaves are species and this assignment captures the diversity
present in the coalition of species considered. We consider the Shapley value
of tree games and suggest a biological interpretation. We determine the linear
transformation M that shows the dependence of the Shapley value on the edge
weights of the tree, and we also compute a null space basis of M. Both depend
on the "split counts" of the tree. Finally, we characterize the Shapley value
on tree games by four axioms, a counterpart to Shapley's original theorem on
the larger class of cooperative games.; Comment: References added, and a section (calculating the Shapley value of a
tree game from its subtrees) was removed for length reasons (request of
referee) and may appear in another paper. 16 pages; related work at
http://www.math.hmc.edu/~su/papers.html. Journal of Mathematical Biology, to
appear. The original article is available at http://www.springerlink.com

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## Bounding the Estimation Error of Sampling-based Shapley Value Approximation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The Shapley value is arguably the most central normative solution concept in
cooperative game theory. It specifies a unique way in which the reward from
cooperation can be "fairly" divided among players. While it has a wide range of
real world applications, its use is in many cases hampered by the hardness of
its computation. A number of researchers have tackled this problem by (i)
focusing on classes of games where the Shapley value can be computed
efficiently, or (ii) proposing representation formalisms that facilitate such
efficient computation, or (iii) approximating the Shapley value in certain
classes of games. For the classical \textit{characteristic function}
representation, the only attempt to approximate the Shapley value for the
general class of games is due to Castro \textit{et al.} \cite{castro}. While
this algorithm provides a bound on the approximation error, this bound is
\textit{asymptotic}, meaning that it only holds when the number of samples
increases to infinity. On the other hand, when a finite number of samples is
drawn, an unquantifiable error is introduced, meaning that the bound no longer
holds. With this in mind, we provide non-asymptotic bounds on the estimation
error for two cases: where (i) the \textit{variance}...

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## The Shapley Value in Knapsack Budgeted Games

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/09/2014
Português

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We propose the study of computing the Shapley value for a new class of
cooperative games that we call budgeted games, and investigate in particular
knapsack budgeted games, a version modeled after the classical knapsack
problem. In these games, the "value" of a set $S$ of agents is determined only
by a critical subset $T\subseteq S$ of the agents and not the entirety of $S$
due to a budget constraint that limits how large $T$ can be. We show that the
Shapley value can be computed in time faster than by the na\"ive exponential
time algorithm when there are sufficiently many agents, and also provide an
algorithm that approximates the Shapley value within an additive error. For a
related budgeted game associated with a greedy heuristic, we show that the
Shapley value can be computed in pseudo-polynomial time. Furthermore, we
generalize our proof techniques and propose what we term algorithmic
representation framework that captures a broad class of cooperative games with
the property of efficient computation of the Shapley value. The main idea is
that the problem of determining the efficient computation can be reduced to
that of finding an alternative representation of the games and an associated
algorithm for computing the underlying value function with small time and space
complexities in the representation size.; Comment: A short version to appear in the 10th Conference on Web and Internet
Economics (WINE 2014)

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## Comparing the rankings obtained from two biodiversity indices: the Fair Proportion Index and the Shapley Value

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/07/2015
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The Shapley Value and the Fair Proportion Index of phylogenetic trees have
been frequently discussed as prioritization tools in conservation biology. Both
indices rank species according to their contribution to total phylogenetic
diversity, allowing for a simple conservation criterion. While both indices
have their specific advantages and drawbacks, it has recently been shown that
both values are closely related. However, as different authors use different
definitions of the Shapley Value, the specific degree of relatedness depends on
the specific version of the Shapley Value - it ranges from a high correlation
index to equality of the indices. In this note, we first give an overview of
the different indices. Then we turn our attention to the mere ranking order
provided by either of the indices. We show that even though the chance of two
rankings being exactly identical (when obtained from different versions of the
Shapley Value) decreases with an increasing number of taxa, the distance
between the two rankings converges to zero, i.e. the rankings are becoming more
and more alike. Moreover, we introduce our software package FairShapley, which
was implemented in Perl and with which all calculations have been performed.; Comment: 19 pages...

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## The Inverse Shapley Value Problem

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/12/2012
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#Computer Science - Computer Science and Game Theory#Computer Science - Computational Complexity#Computer Science - Data Structures and Algorithms

For $f$ a weighted voting scheme used by $n$ voters to choose between two
candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of
$f$ provide a measure of how much control each voter can exert over the overall
outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley
and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice
theory as a measure of the "influence" of voters. The \emph{Inverse Shapley
Value Problem} is the problem of designing a weighted voting scheme which
(approximately) achieves a desired input vector of values for the
Shapley-Shubik indices. Despite much interest in this problem no provably
correct and efficient algorithm was known prior to our work.
We give the first efficient algorithm with provable performance guarantees
for the Inverse Shapley Value Problem. For any constant $\eps > 0$ our
algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is
independent of $\eps$) and has the following performance guarantee: given as
input a vector of desired Shapley values, if any "reasonable" weighted voting
scheme (roughly, one in which the threshold is not too skewed) approximately
matches the desired vector of values to within some small error...

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## How good is the Shapley value-based approach to the influence maximization problem?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/09/2014
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#Computer Science - Artificial Intelligence#Computer Science - Multiagent Systems#Computer Science - Social and Information Networks#I.2.1

The Shapley value has been recently advocated as a method to choose the seed
nodes for the process of information diffusion. Intuitively, since the Shapley
value evaluates the average marginal contribution of a player to the
coalitional game, it can be used in the network context to evaluate the
marginal contribution of a node in the process of information diffusion given
various groups of already 'infected' nodes. Although the above direction of
research seems promising, the current liter- ature is missing a throughout
assessment of its performance. The aim of this work is to provide such an
assessment of the existing Shapley value-based approaches to information
diffusion.; Comment: 21st European Conference on Artificial Intelligence

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## Implementation of the Ordinal Shapley Value for a three-agent economy

Fonte: Conselho Superior de Investigações Científicas
Publicador: Conselho Superior de Investigações Científicas

Tipo: Documento de trabajo

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We propose a simple mechanism that implements the Ordinal Shapley Value (Pérez-Castrillo and Wettstein [2005]) for economies with three or less agents.; We gratefully acknowledge financial support from project BEC 2003-01133, the Generalitat
de Catalunya (2001 SGR-00162 and Barcelona Economics, CREA), and the Israeli Science
Foundation.

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## An Ordinal Shapley Value for Economic Environments [Revised Version]

Fonte: Elsevier
Publicador: Elsevier

Tipo: Documento de trabajo

Português

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Revised Version of the Paper UFAE and IAE Working Papers nr. 560.03. Published in the Journal of Economic Theory, Vol. 127, Issue 1, March 2006, Pages 296-308.; We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

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## Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value

Fonte: Conselho Superior de Investigações Científicas
Publicador: Conselho Superior de Investigações Científicas

Tipo: Documento de trabajo

Português

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We propose a simple mechanism to determine how the surplus generated by cooperation is to be shared in zero-monotonic environments with transferable utility. The mechanism consists of a bidding stage followed by a proposal stage. We show that the
subgame perfect equilibrium outcomes of this mechanism coincide with the vector of the Shapley value payoffs. We extend our results to implement the weighted Shapley values. Finally, we generalize our mechanism to handle arbitrary transferable utility environments. The modified mechanism generates an efficient coalition structure, and implements the Shapley values of the super-additive cover of the environment.; Pérez-Castrillo acknowledges financial support from the DGES PB 97-0181 and SGR 96-75. Part of this research was conducted while Wettstein was visiting the Universitat Autònoma de Barcelona, with a grant from the Generalitat de Catalunya, and both authors were visiting the University of Copenhagen, whose financial support is acknowledged.

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## An Ordinal Shapley Value for Economic Environments

Fonte: Conselho Superior de Investigações Científicas
Publicador: Conselho Superior de Investigações Científicas

Tipo: Documento de trabajo

Português

Relevância na Pesquisa

68.315195%

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions "measuring" the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.; Pérez-Castrillo gratefully acknowledges financial support from projects BEC
2000-0172 and 2001 SGR-00162. Part of this research was conducted while Wettstein was visiting the Universitat Autònoma de Barcelona, with a grant from the Generalitat de Catalunya.; Peer reviewed

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## An ordinal shapley value for economic environments (Revised version)

Fonte: Universidade Autônoma de Barcelona
Publicador: Universidade Autônoma de Barcelona

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em //2006
Português

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We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

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## An ordinal shapley value for economic environments

Fonte: Universidade Autônoma de Barcelona
Publicador: Universidade Autônoma de Barcelona

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em //2006
Português

Relevância na Pesquisa

48.162188%

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.

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## Proposta metodológica de cobrança pelo uso dos recursos hídricos usando o valor de Shapley: uma aplicação à bacia do rio Paraíba do Sul

Fonte: Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade
Publicador: Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade

Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion;
Formato: application/pdf

Publicado em 01/09/2010
Português

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#water resources#cost allocation#Shapley value#river basin#recursos hídricos#alocação de custos#valor de Shapley#bacia hidrográfica

This study aimed to propose a methodology for charging for the use of water resources based on the allocation of costs - among sectors that demand water - of projects related to improvements in a river basin. This methodology consists of a rule of allocation known as Shapley value, belonging to the theory of cooperative games, and to show its applicability, we performed a case study in a sub-basin of the Paraíba do Sul river basin. As criteria for allocation of costs, we used the volumes of water withdrawn and consumed, and the amount of effluent discharged into the river. In applying the methodology, we considered three different scenarios: "clean" basin, polluted basin, and an intermediate situation, closer to real situation now found in the sub-basin analyzed. The obtained results showed high dependence of the cost allocation criteria (weights assigned to the volumes of water withdrawn and consumed, and the quantity of effluent discharged), and, in the case of intermediate scenario considered, the values found indicate that the urban users should pay the greatest part of the costs when compared to the fees currently in use, since these users are among those that greatly discharge effluents, being the deterioration of water quality the most relevant problem in this basin.; Este trabalho teve como objetivo propor uma metodologia de cobrança pelo uso de recursos hídricos baseada na alocação de custos - entre os setores demandantes de água - de projetos relacionados com melhorias em uma bacia hidrográfica. Essa metodologia consiste em regra de alocação conhecida como valor de Shapley...

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