Monotonic solutions of cooperative games

By H. Peyton Young. 1985

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

A Unified Approach to Interpreting Model Predictions (2017, background): “Young (1985) demonstrated that Shapley values are the only set of values that satisfy three axioms similar to Property 1, Property 3, and a ﬁnal property we show is redundant in this setting (see Supplementary material).”
An unexpected unity among methods for interpreting model predictions (2016, background): “In 1985, Peyton Young demonstrated that there is only one set of values that satisﬁes the above assumptions and they are the Shapley values [7, 4].”
Algorithmic Transparency via Quantitative Input Influence: Theory and Experiments with Learning Systems (2016, background): “[19] offers an alternative characterization of the Shapley value, based on the more natural monotonicity assumption, which is a strong generalization of the dummy axiom.”
The Shapley Value (1994, background): “" Not much, " according to Young (1985), whose finding also yields an alternative axiomatization of the value.”
Axiomatic arguments for decomposing goodness of fit according to Shapley and Owen values (2012, background): “Theorem 1 (Young [24]) The Shapley value is the only rule that satisfies Efficiency, Monotonicity, and the Equal treatment property.”
Explaining individual predictions when features are dependent: More accurate approximations to Shapley values (2019, unknown): “By summarizing the right hand sides above, we easily see that they add up to the total worth of the game: The Shapley value has the following desirable properties: Eﬃciency: The total gain is distributed Symmetry: If i and j are two players who contribute equally to all possible coalitions, i.e.”
On the Impossibility of Fair Risk Allocation (2010, methodology): “monotonicity and CC was also examined by Young (1985) and Housman and Clark (1998).”
Null players, solidarity, and the egalitarian Shapley values (2013, background): “6 This axiom is a relaxation of the well-known monotonicity axiom (Young, 1985) in the sense that its implication only is supposed to hold if v (N) w (N).”
Explaining by Removing: A Unified Framework for Model Explanation (2020, background): “This is a stronger version of the marginalism property introduced by Young’s axiomatization of the Shapley value (Young, 1985), and solution concepts of this form are known as probabilistic values (Weber, 1988).”
Algorithms to estimate Shapley value feature attributions (2022, background): “Furthermore, they are a unique solution to the credit allocation problem as defined by several desirable properties [35, 42] (Figure 2b).”
The Explanation Game: Explaining Machine Learning Models with Cooperative Game Theory (2019, methodology): “ value method is the unique method satisfying four desirable axioms: Dummy ,Symmetry Efﬁciency, and Linearity. We informally describe the axioms in the Supplemental Material, and refer the reader to (Young 1985) for formal deﬁnitions and proofs. The rest of this paper deals with the application of S”
L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data (2018, background): “It can be justiﬁed on an axiomatic basis [18, 24] as being the unique function from a collection of 2 d numbers (one for each subset S ) to a collection of d numbers (one for each feature i ) with the following properties: Monotonicity: Given two models P m and P m , let m x and m x denote the…”
Explainable AI for Trees: From Local Explanations to Global Understanding (2019, background): “The equivalent of Theorem 1 has been previously presented in [41] and follows from cooperative game theory results [76], where the values φi are known as the Shapley values [63].”
Fifty years of the nash program,1953-2003 (2004, background): “In Young (1985), a marginality axiom serves to characterize the Shapley value, together with efficiency and symmetry – Shapley’s and Young’s theorems are to be viewed in parallel: while the former derives the marginal formula from additivity, the latter obtains the linear dependence on the marginal…”