Related papers: On Reward-Penalty-Selection Games

A natural partial ordering exists on the set of all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper…

We study $n$-player turn-based games played on a finite directed graph. For each play, the players have to pay a cost that they want to minimize. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame…

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…

We study a class of probabilistic cooperative games which can be treated as an extension of the classical cooperative games with transferable utilities. The coalitions have an exogenous probability of being realized. This probability…

We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that…

The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected,…

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…

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…

The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every…

Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum cardinality of independent sets in the subgraph defined by the coalition. In this paper, we investigate the…

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…

This paper studies how to attain fairness in communication for omniscience, where a set of users exchange their observations of a discrete multiple random source to attain omniscience---the state that all users recover the entire source.…

We propose a decentralized solution for a pursuit-evasion game involving a heterogeneous group of rational (selfish) pursuers and a single evader based on the framework of potential games. In the proposed game, the evader aims to delay (or,…

Hedonic games are a prominent model of coalition formation, in which each agent's utility only depends on the coalition she resides. The subclass of hedonic games that models the formation of general partnerships, where output is shared…

We study the approximate core for edge cover games, which are cooperative games stemming from edge cover problems. In these games, each player controls a vertex on a network $G = (V, E; w)$, and the cost of a coalition $S\subseteq V$ is…

Identifying critical nodes in complex networks is a fundamental task in graph mining. Yet, methods addressing an all-or-nothing coverage mechanics in a bipartite dependency network, a graph with two types of nodes where edges represent…

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 game of Cops and Robber is a pursuit-evasion game which is usually played on a connected graph. In the game, a set of cops and a robber move around the vertices of a graph along edges, where the cops aim to capture the robber, while the…

The range of a payoff function for an $n$-player finite strategic game is investigated using a novel approach, the notion of extreme points of a non-convex set. The shape of a noncooperative payoff region can be estimated using extreme…

Many interactions result in a socially suboptimal equilibrium, or in a non-equilibrium state, from which arriving at an equilibrium through simple dynamics can be impossible of too long. Aiming to achieve a certain equilibrium, we persuade,…