Minority reserves are an affirmative action policy proposed by Hafalir et al. [20] in the context of school choice. We study in the laboratory the effect of minority reserves on the outcomes of two prominent matching mechanisms, the Gale-Shapley and the Top Trading Cycles mechanisms. Our first experimental result is that the introduction of minority reserves enhances truth-telling of some minor...

In this paper, a general expression of the Shapley value for fuzzy games on vague sets is proposed, where the player participation levels are vague sets. The existence and uniqueness of the given Shapley value are showed by establishing axiomatic system. When the fuzzy games on vague sets are convex, the given Shapley value is a vague population monotonic allocation function (VPMAF) and an elem...

We concern the problem of matching the agents from two disjoint sets, such that the agents from the first set have preferences over the agents from the second set and vice versa. Typical problems of this sort are: college admissions problem, matching workers with firms, men with women (in a matrimonial agency) and so on. Classical approach to this problem comes from Gale and Shapley (1962). Rec...

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 priori evaluation of the prospects of a group of players in a coalitional game when acting as a unit. We study its properties and we give an axiomatic charact...

We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote process. We characterize the impact of changing the quota (i.e., the minimum number of seats in the parliament that are required to form a coalition) on the...

coalitional game deals with situations that involve cooperations among players, and there are different solution concepts such as the core,the shapley value and the kernel. in many situations, there is no way to predict the payoff functions except for the expert experiencesand subjective intuitions, which leads to the coalitional game with fuzzy payoffs. within the framework of credibility theo...

It is shown that the graphs for which the Szeged index equals ‖G‖·|G| 2 4 are precisely connected, bipartite, distance-balanced graphs. This enables to disprove a conjecture proposed in [Some new results on distance-based graph invariants, European J. Combin. 30 (2009) 1149–1163]. Infinite families of counterexamples are based on the Handa graph, the Folkman graph, and the Cartesian product of ...

The paper starts by proposing an explicit and intuitive bargaining process to analyze coalitional externalities, which we then use to generate a value allocation extending the Shapley value to partition function from games, the Rational Belief Shapley value (RBS). We investigate the strategic foundation of the value by constructing a mechanism implementing it. It extends existing models of mult...

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...