Data envelopment analysis (DEA) is an effective tool for supporting decision-makers to assess bankruptcy, uncertainty concepts including intervals, and game theory. The bankruptcy problem with the qualitative parameters is an economic problem under uncertainty. Accordingly, we combine the concepts of the DEA game theory and uncertain models as interval linear programming (ILP), which can be app...

We consider the problem of the axiomatization of the Shapley value on the class of assignment games. We show that Shapley’s original [21], Young’s [24], Chun’s [7], van den Brink’s [2], (5-6) Hart and Mas-Colell’s [12] potential function and consistency approaches and Roth’s [19] characterization do not work on the class of assignment games. We also consider Myerson’s [15] axiomatization of the...

It is well known since Owen (1968) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e., of the ability to bargain) of the players. This paper proposes a new weight scheme for the Shapley value. Weights in this framework have to be interpreted as a measure of bargaining power. Two different axiomatic characterizations of this new value are proposed: o...

This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to construct a characteristic function via the filled ballot paper profile of voters. The Shapley value serves as the ranking method. The winner is the candidate havi...

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...

One of the main issues in economics is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide tools that make it possible to study this trade-off in a consistent way by providing three types of results on egalitari...

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In t...

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache’s axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value ...

Drawing on insights about the geometric structure of majority rule spatial voting games with Euclidean preferences derived from the Shapley– Owen value (Shapley and Owen, Int J Game Theory 18:339–356, 1989), we seek to explain why the outcomes of experimental committee majority rule spatial voting games are overwhelmingly located within the uncovered set (Bianco et al. We suggest that it is not...

Graph-restricted games, first introduced by Myerson [20], model naturally-occurring scenarios where coordination between any two agents within a coalition is only possible if there is a communication channel(a path) between them. Two fundamental solution concepts that were proposed for such a game are the Shapley value and the Myerson value. While an algorithm has been proposed to compute the S...