Related papers: Balanced contributions, consistency, and value for…
One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central…
The Shapley value is one of the most important solution concepts in cooperative game theory. In coalitional games without externalities, it allows to compute a unique payoff division that meets certain desirable fairness axioms. However, in…
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 show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be 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…
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…
Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…
We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for…
Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…
In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…
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…
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…
For networks with externalities, where each component's worth may depend on the full network structure, balanced contributions and fairness lead to distinct component-efficient allocation rules. We characterize the unique…
We consider the problem of designing distribution rules to share "welfare" (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this…
We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is…
Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
This study introduces the \emph{edge-based Shapley value}, a novel allocation rule within cooperative game theory, specifically tailored for networked systems, where value is generated through interactions represented by edges. Traditional…
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…
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…