Related papers: Necessary players and values
In cooperative games with transferable utilities, the Shapley value is an extreme case of marginalism while the Equal Division rule is an extreme case of egalitarianism. The Shapley value does not assign anything to the non-productive…
In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with level structures. In the case of the equal…
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…
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…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
We explore a broad class of values for cooperative games in characteristic function form, known as \emph{compromise values\/}. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs.…
In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal…
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…
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…
This paper studies multiplayer turn-based games on graphs in which player preferences are modeled as $\omega$-automatic relations given by deterministic parity automata. This contrasts with most existing work, which focuses on specific…
We introduce and study the axiom of null player neutrality in the context of cooperative games with transferable utility (TU-games). This axiom weakens the classical coalitional strategic equivalence: rather than requiring that augmenting a…
Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…
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, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is…
The Owen value is an well-known allocation rule for cooperative games with coalition structure.In this paper, we introduce the concept of highly mutually dependent unions. Two unions in a cooperative game with coalition structure are said…
We show that a cooperative game may be decomposed into a sum of component games, one for each player, using the combinatorial Hodge decomposition on a graph. This decomposition is shown to satisfy certain efficiency, null-player, symmetry,…
We define a notion of the criticality of a player for simple monotone games based on cooperation with other players, either to form a winning coalition or to break a winning one, with an essential role for all the players involved. We…
We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…
In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by…
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…