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Variance decompositions for extensive-form games
[article]

2020
*
arXiv
*
pre-print

We treat the outcome of a

arXiv:2009.04834v1
fatcat:yma4jjahrzgqlchisx44n3wuiq
*game*as a random variable and derive a closed-*form*expression and estimator*for*the*variance*in the outcome attributable to a player of the*game*. ... A simple example is given to demonstrate how*variance**decompositions*can be used to measure other interesting properties of*games*. ...*Variance**decompositions**for**game*outcomes*Extensive*-*form**games*with random variables*For*convenience, we introduce random variables that represent the actions selected by players in a single play of ...##
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Inequality decomposition values: the trade-off between marginality and efficiency

2011
*
Journal of Economic Inequality
*

The methods of

doi:10.1007/s10888-011-9207-y
fatcat:cxo7m4557nhjpcyje7gnjzorwe
*decomposition*proposed are based on the Shapley value and*extensions*of the Shapley value of transferable utility cooperative*games*. ... This paper presents a general procedure*for*decomposing income inequality measures by income sources. ... Shorrocks*for*a discussion which has revived our interest in this topic. ...##
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Income inequality games

2011
*
Journal of Economic Inequality
*

We also investigate the case of multiplicative poverty

doi:10.1007/s10888-011-9184-1
fatcat:7zheb3if2zcrde75icza666z2u
*games**for*which indices are non additively decomposable in order to capture contributions of sub-indices, which are multiplicatively connected with ... We first investigate the problem of source*decomposition*of inequality measures, the so-called additive income sources inequality*games*, baed on the Shapley Value, introduced by Chantreuil and Trannoy ...*For*instance the natural*decomposition*of the*variance*(see the Introduction) yields,*for*source , an absolute natural contribution of cov(x , x) =: S . I(·) satisfies (UA) S y ≤ 0. ...##
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Variance Allocation and Shapley Value

2017
*
Methodology and Computing in Applied Probability
*

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-

doi:10.1007/s11009-016-9540-5
fatcat:5mx222ygpvbmdoy2gtegsvlc7u
*variance*choice paradigm, we propose an allocation criterion*for*the*variance*of the sum of n possibly dependent random ... The main result of this paper shows that in our particular case the Shapley value has a very simple*form*that can be easily computed. ... In the following we show that the characteristic function of the*variance**game*respects their*decomposition*requirements. ...##
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Relative Importance and Value

2005
*
Social Science Research Network
*

Proportional Marginal

doi:10.2139/ssrn.2255827
fatcat:yp6fgn2ggzfafbf6aj273bh4tm
*Decomposition*Proportional marginal*decomposition*takes a very intuitive*form*in two variable models (with no intercept). ... Then CV D(w) = Sh(w). 8 See,*for*example, There is another relationship between covariance*decomposition*and cooperative*game*theory. ...##
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Stochastic selfish routing

2012
*
ACM SIGecom Exchanges
*

(

doi:10.1145/2325713.2325717
fatcat:xd5wh5iysbcv3n5g2ihx3jqrjm
*For*example, even computing players' best responses has an unknown complexity [24] .) ... We prove that under exogenous stochastic delays, the price of anarchy is exactly the same as in the corresponding*game*with deterministic delays. ... Acknowledgements We thank Hari Balakrishnan, José Correa and Costis Daskalakis*for*helpful discussions. ...##
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Stochastic Selfish Routing
[chapter]

2011
*
Lecture Notes in Computer Science
*

(

doi:10.1007/978-3-642-24829-0_28
fatcat:bcaywmtuandlpikdmlglkuhvxu
*For*example, even computing players' best responses has an unknown complexity [24] .) ... We prove that under exogenous stochastic delays, the price of anarchy is exactly the same as in the corresponding*game*with deterministic delays. ... Acknowledgements We thank Hari Balakrishnan, José Correa and Costis Daskalakis*for*helpful discussions. ...##
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The evolution of altruism: Game theory in multilevel selection and inclusive fitness

2007
*
Journal of Theoretical Biology
*

The model also suggests a simple interpretation of the Price selection

doi:10.1016/j.jtbi.2006.09.030
pmid:17087973
fatcat:bmedaq2nqbhm5hrevzs5fuk2ni
*decomposition*and an alternative*decomposition*that is symmetrical and complementary to it. ... Although the prisoner's dilemma (PD) has been used*extensively*to study reciprocal altruism, here we show that the n-player prisoner's dilemma (NPD) is also central to two other prominent theories of the ... The resulting actual DQ*for*this run exactly matches the alt DQ W component given by the alternative*decomposition*. ...##
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A Non-Negative Matrix Factorization Game
[article]

2021
*
arXiv
*
pre-print

We present a novel

arXiv:2104.05069v1
fatcat:lpktbv4mbncbbmiootqy5ztgz4
*game*-theoretic formulation of Non-Negative Matrix Factorization (NNMF), a popular data-analysis method with many scientific and engineering applications. ... The*game*-theoretic formulation is shown to have favorable scaling and parallelization properties, while retaining reconstruction and convergence performance comparable to the traditional Multiplicative ... Lillian Ratliff*for*helpful discussions. ...##
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A note on the Sobol' indices and interactive criteria

2017
*
Fuzzy sets and systems (Print)
*

We also relate the latter to the Banzhaf interaction transform and compute the Sobol' indices

doi:10.1016/j.fss.2016.05.009
fatcat:qxhylsshwrhjxbat4dhmauxvzm
*for*the 2-additive Choquet integral. ... We consider in this note another approach to define interaction, by using the Sobol' indices which are related to the analysis of*variance*of a multivariate model. ... A classical basis of R 2 N is the basis of the unanimity*games*.*For*any nonempty subset S ⊆ N , the unanimity*game*centered on S is the*game*defined by u S (T ) = 1, if T ⊇ S 0, otherwise . ...##
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Page 4553 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

We introduce a class of models that are based on an

*extension*of*game*-theoretic models, defined by a*game*in general*form*, and their mappings into a class of algebraic systems. ... With the use of certain formulas of Ramanujan found in his second notebook, an asymptotic formula*for*the*variance*of Xy is proved. ...##
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Page 855 of Mathematical Reviews Vol. , Issue 80B
[page]

1980
*
Mathematical Reviews
*

A topology

*for*time-*variance*in general is then introduced. ...*Extensions*of these ideas to nonlinear nonquadratic problems are explored and relations of the control concepts developed here to differential*game*strategies are also discussed. ...##
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External correspondence: Decompositions of the mean probability score

1982
*
Organizational Behavior and Human Performance
*

Requests

doi:10.1016/0030-5073(82)90237-9
fatcat:qohqachdi5c2bm73j5zzskkvbe
*for*reprints should be sent to ... Yates, Forecasting performance: A covariance*decomposition*of the mean probability score. ... The outcome index*variance*, d(1 -d), provides a good reference point*for*interpreting PS. ...##
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Learning to Represent Action Values as a Hypergraph on the Action Vertices
[article]

2021
*
arXiv
*
pre-print

We show the effectiveness of our approach on a myriad of domains: illustrative prediction problems under minimal confounding effects, Atari 2600

arXiv:2010.14680v2
fatcat:qyg44x7wvfd6fizogxypfg5h2m
*games*, and discretised physical control benchmarks. ... We conjecture that leveraging the combinatorial structure of multi-dimensional action spaces is a key ingredient*for*learning good representations of action. ... ACKNOWLEDGEMENTS We thank Ileana Becerra*for*insightful discussions, Nemanja Rakicevic and Fabio Pardo*for*comments on the manuscript, Fabio Pardo*for*providing the DDPG results which he used*for*benchmarks ...##
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Page 5032 of Mathematical Reviews Vol. , Issue 95h
[page]

1995
*
Mathematical Reviews
*

On finding optimal policies

*for*Markov decision chains: a unifying framework*for*mean-*variance*-tradeoffs. (English summary) Math. Oper. Res. 19 (1994), no. 2, 434-448. ... bounded mean and mean penalized by*variance*. ...
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