Values of Non-Atomic Games

By R. Aumann, Lloyd S. Shapley. 1974

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In Game & Decision Theory

Citations in the corpus

Axiomatic Attribution for Deep Networks (2017, methodology): “Integrated gradients correspond to a cost-sharing method called Aumann-Shapley (Aumann & Shapley, 1974).”
Dynamic capital allocation with distortion risk measures (2004, unknown): “Tsanakas and Barnett (2002) employed concepts from cooperative game theory (Aumann and Shapley, 1974) for the allocation of risk capital to portfolios of pooled liabilities, when distortion risk measures (Wang et al.”
Existence of a solution to an equation arising from the theory of Mean Field Games (2015, background): “In this pioneering work, Aumann–Shapley proposed a profound mathematical theory for economics, the potential of which has not yet been fully exploited.”
Coherent allocation of risk capital (2001, background): “Aumann and Shapley’s book “Values of Non-Atomic Games” [ 7 ] was the”
To Split or Not to Split: Capital Allocation with Convex Risk Measures (2007, unknown): “The Aumann-Shapley value (Aumann and Shapley, 1974), originating in cooperative game theory, is proposed as an appropriate capital allocation mechanism. The AumannShapley allocation can be viewed as a genaralisation of marginal costs that is applicable even when the risk measure is not homogenous. I”
Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities (2003, unknown): “Cooperative game theory (Shapley (1953), Aumann and Shapley (1974), Aubin (1981)) provides a suitable framework for cost allocation problems (e.g. Lemaire 1984). Typically, provisions are made so that the allocation of total costs does not produce disincentives for cooperation to any player (instrum”
Gradients of Counterfactuals (2016, methodology): “The specific path we use corresponds to a cost-sharing method called Aumann-Shapley (Aumann & Shapley (1974)).”
Inclines and incline matrices: a survey (2004, methodology): “Continuous linearly ordered inclines on [0, 1] such that 02 = 0, 12 = 1 must be commutative, and in fact they can in a certain sense all be built out of our three fundamental inclines:”
The many Shapley values for model explanation (2019, methodology): “n is that the features are distributed according to "the distribution generated by the tree". 2 9. [19] proposes a technique called Integrated Gradients, that is based on the Aumann-Shapley [4] cost-sharing technique. Aumann-Shapley is one of the several extensions of the discrete Shapley ”
A Universal Integral as Common Frame for Choquet and Sugeno Integral (2010, background): “To be precise, normed monotone measures on (X, A), i.e., monotone measures satisfying m(X )=1 , are also called fuzzy measures [19], [64], [68], [69], or capacities [19] or (monotone) games [ 2 ], [7], depending on the context.”
Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation (2019, methodology): “Integrated Gradients (Sun-dararajan et al., 2017), on the other hand, can be shown to compute Aumann-Shapley values (Aumann & Shapley, 1974), an extension of Shapley values for inﬁnite games where each individual player has a negligible contribution.”
Subcalculus for set functions and cores of TU games (2003, background): “This has motivated a large literature on non-additive set functions in both game and decision theory, which includes the classic book of Aumann and Shapley (1974). In mathematics as well, non-additive set functions have been the subject of many investigations, mostly in the wake of the seminal work ”
Influence-Directed Explanations for Deep Convolutional Networks (2018, methodology): “This approach is inspired, in part, by axiomatic justification for power indices in cooperative game theory [13], [14]–an approach that has been previously employed for explaining predictions of machine learning models [15], [3].”