Related papers: The Shapley-Hodge Associated Game
Hyperparameter optimization (HPO) is a crucial step in achieving strong predictive performance. Yet, the impact of individual hyperparameters on model generalization is highly context-dependent, prohibiting a one-size-fits-all solution and…
Additively separable hedonic games (ASHGs) are a prominent model of coalition formation where agents' preferences are derived from their individual valuations of peers. While social welfare maximization in ASHGs has traditionally focused…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…
A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…
Shapley values have become increasingly popular in the machine learning literature thanks to their attractive axiomatisation, flexibility, and uniqueness in satisfying certain notions of `fairness'. The flexibility arises from the myriad…
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,…
This paper introduces the class of cooperative games with generalized coalition configuration. This new class of games corresponds to cooperative games with coalition configuration and restricted cooperation. A coalition configuration is a…
Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. Spatial facility location models have successfully predicted the outcome of…
In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify…
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…
Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian…
Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…
We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an…
Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge…
The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…
The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has…
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,…
In this paper, we introduce an agent-based representation of games, in order to propose a compact representation for multi-party games in game theory. Our method is inspired by concepts in process theory and process algebra. In addition, we…
In this paper, we study the total displacement statistic of parking functions from the perspective of cooperative game theory. We introduce parking games, which are coalitional cost-sharing games in characteristic function form derived from…