2022/07/12 by Tomáš Kroupa, Kroupa, Tomáš, Sara Vannucci +3
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #91A12 #91A80 #94A15 #94A17 #Bayesian Modeling and Causal Inference #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Voting Systems #Information Theory (cs.IT) #Multi-Criteria Decision Making
paper · pdf · doi:10.48550/arxiv.2207.05519
openalex publication_date 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The information decomposition problem requires an additive decomposition of the mutual information between the input and target variables into nonnegative terms. The recently introduced solution to this problem, Information Attribution, involves the Shapley-style value measuring the influence of predictors in the coalitional game associated with the joint probability distribution of the input random vector and the target variable. Motivated by the original problem, we consider a general setting of coalitional games where the players form a boolean algebra, and the coalitions are the corresponding down-sets. This enables us to study in detail various single-valued solution concepts, called values. Namely, we focus on the classes of values that can represent very general alternatives to the solution of the information decomposition problem, such as random-order values or sharing values. We extend the axiomatic characterization of some classes of values that were known only for the standard coalitional games.