Related papers: Shapley-like values without symmetry
In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called \emph{weak saddle}. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence,…
The Shapley value is a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…
In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit…
The purpose of this study is to propose a model that predicts the social and psychological factors that affect the individuals collaborative learning outcome in group projects. The model is established on the basis of two theories, namely,…
In this paper we consider strategic cost sharing games with so-called arbitrary sharing based on various combinatorial optimization problems, such as vertex and set cover, facility location, and network design problems. We concentrate on…
Not all real-world data are labeled, and when labels are not available, it is often costly to obtain them. Moreover, as many algorithms suffer from the curse of dimensionality, reducing the features in the data to a smaller set is often of…
We study the notion of efficiency for cooperative games on simplicial complexes. In such games, the grand coalition $[n]$ may be forbidden, and, thus, it is a non-trivial problem to study the total number of payoff $v_{\Delta}$ of a…
The presence of artificial intelligence (AI) in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images,…
The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the…
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents'…
In cooperative games, we study how values created or costs incurred by a coalition are shared among the members within it, and the players may join the coalition in a online manner such as investors invest a startup. Recently, Ge et al.…
We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual…
Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation…
Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…
This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated…
As the use of complex machine learning models continues to grow, so does the need for reliable explainability methods. One of the most popular methods for model explainability is based on Shapley values. There are two most commonly used…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…