Related papers: The Shapley Value in the Knaster Gain Game
The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…
The Shapley value is arguably the most central normative solution concept in cooperative game theory. It specifies a unique way in which the reward from cooperation can be "fairly" divided among players. While it has a wide range of real…
In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation…
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…
The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…
This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the…
This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's…
We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it…
We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney…
The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This…
We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's conception introduced a bargaining solution that minimises the maximal quantified ``propensity to disrupt'' the negotiation process of the…
As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…
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…
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…
Incentives for early arrival (I4EA) was recently proposed for studying online cooperative games. In an online cooperative game, players arrive in an unknown order, and the value increase after each player arrived should be distributed…
We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…
Cooperative game theory deals with systems where players want to cooperate to improve their payoffs. But players may choose coalitions in a non-cooperative manner, leading to a coalition-formation game. We consider such a game with several…
Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study…
In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that…
Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important…