Coalition formation is an important capability for automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Coalitional game theory provides a number of solution concepts for this. However, recent research has revealed that these traditional solution concepts are vulner...

In the theory of cooperative transferable utilities games, (TU games), the Efficient Values, that is those which show how the win of the grand coalition is shared by the players, may not be a good solution to give a fair outcome to each player. In an earlier work of the author, the Inverse Problem has been stated and explicitely solved for the Shapley Value and for the Least Square Values. In t...

The concept of Shapley values was first introduced into the game theory by Shapley [1953] in the framework of transferable payoffs, playing an important role in the game theory. According to a standard textbook on game theory it is interpreted as in what follows. “Suppose that all the players are arranged in some order, all orders being equally likely. Then player i’s Shapley value is the expec...

The aim of the present paper is to study a one-point solution concept for bicooperative games. For these games introduced by Bilbao (Cooperative Games on Combinatorial Structures, 2000), we define a one-point solution called the Shapley value, since this value can be interpreted in a similar way to the classical Shapley value for cooperative games. The main result of the paper is an axiomatic c...

We examine the characterization of the Shapley value that was introduced by Young and refined later by Neyman. A new proof of this axioma-tization is given and as an illustration of the new proof it is demonstrated that the axioms under consideration characterize the Shapley value on various well-known classes of T U games.

Feature attributions based on the Shapley value are popular for explaining machine learning models. However, their estimation is complex from both theoretical and computational standpoints. We disentangle this complexity into two main factors: approach to removing feature information tractable strategy. These factors provide a natural lens through which we can better understand compare 24 disti...

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 Knaster (1946). In this paper we analyze the Shapley value (Shapley, 1953) of the game and propose its use as a measure of the players’ attitude towards coll...

The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game inwhich cooperation of all players in a given coalition yields payoff.We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, whenwe express a game by a line...

Shapley value is a popular way to compute payoffs in cooperative games where the agents are assumed to have deterministic, risk-neutral (linear) utilities.This paper explores a class of Multi-agent constantsum cooperative games where the payoffs are random variables. We introduce a new model based on Borch’s Theorem from the actuarial world of re-insurance, to obtain a Pareto optimal allocation...