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We treat the outcome of a 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 ...arXiv:2009.04834v1 fatcat:yma4jjahrzgqlchisx44n3wuiq
The methods of 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. ...doi:10.1007/s10888-011-9207-y fatcat:cxo7m4557nhjpcyje7gnjzorwe
We also investigate the case of multiplicative poverty 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. ...doi:10.1007/s10888-011-9184-1 fatcat:7zheb3if2zcrde75icza666z2u
Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-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. ...doi:10.1007/s11009-016-9540-5 fatcat:5mx222ygpvbmdoy2gtegsvlc7u
Proportional Marginal 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. ...doi:10.2139/ssrn.2255827 fatcat:yp6fgn2ggzfafbf6aj273bh4tm
(For example, even computing players' best responses has an unknown complexity  .) ... 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. ...doi:10.1145/2325713.2325717 fatcat:xd5wh5iysbcv3n5g2ihx3jqrjm
Lecture Notes in Computer Science
(For example, even computing players' best responses has an unknown complexity  .) ... 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. ...doi:10.1007/978-3-642-24829-0_28 fatcat:bcaywmtuandlpikdmlglkuhvxu
The model also suggests a simple interpretation of the Price selection 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. ...doi:10.1016/j.jtbi.2006.09.030 pmid:17087973 fatcat:bmedaq2nqbhm5hrevzs5fuk2ni
We present a novel 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. ...arXiv:2104.05069v1 fatcat:lpktbv4mbncbbmiootqy5ztgz4
We also relate the latter to the Banzhaf interaction transform and compute the Sobol' indices 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 . ...doi:10.1016/j.fss.2016.05.009 fatcat:qxhylsshwrhjxbat4dhmauxvzm
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. ...
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. ...
Requests 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. ...doi:10.1016/0030-5073(82)90237-9 fatcat:qohqachdi5c2bm73j5zzskkvbe
We show the effectiveness of our approach on a myriad of domains: illustrative prediction problems under minimal confounding effects, Atari 2600 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 ...arXiv:2010.14680v2 fatcat:qyg44x7wvfd6fizogxypfg5h2m
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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