The Shapley Value in the Knaster Gain Game

In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a coopera- tive 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 collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players' evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism

The Ranking Problem of Alternatives as a Cooperative Game

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 having the maximum Shapley value. And finally, we explore the properties of the designed ranking procedure

Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

On the Shapley value and its application to the Italian VQR research assessment exercise

Research assessment exercises have now become common evaluation tools in a number of countries. These exercises have the goal of guiding merit-based public funds allocation, stimulating improvement of research productivity through competition and assessing the impact of adopted research support policies. One case in point is Italy's most recent research assessment effort, VQR 2011–2014 (Research Quality Evaluation), which, in addition to research institutions, also evaluated university departments, and individuals in some cases (i.e., recently hired research staff and members of PhD committees). However, the way an institution's score was divided, according to VQR rules, between its constituent departments or its staff members does not enjoy many desirable properties well known from coalitional game theory (e.g., budget balance, fairness, marginality). We propose, instead, an alternative score division rule that is based on the notion of Shapley value, a well known solution concept in coalitional game theory, which enjoys the desirable properties mentioned above. For a significant test case (namely, Sapienza University of Rome, the largest university in Italy), we present a detailed comparison of the scores obtained, for substructures and individuals, by applying the official VQR rules, with those resulting from Shapley value computations. We show that there are significant differences in the resulting scores, making room for improvements in the allocation rules used in research assessment exercises

College admissions and the role of information : an experimental study

We analyze two well-known matching mechanisms—the Gale-Shapley, and the Top Trading Cycles (TTC) mechanisms—in the experimental lab in three different informational settings, and study the role of information in individual decision making. Our results suggest that—in line with the theory—in the college admissions model the Gale-Shapley mechanism outperforms the TTC mechanisms in terms of efficiency and stability, and it is as successful as the TTC mechanism regarding the proportion of truthful preference revelation. In addition, we find that information has an important effect on truthful behavior and stability. Nevertheless, regarding efficiency, the Gale-Shapley mechanism is less sensitive to the amount of information participants hold

School Choice and Information An Experimental Study on Matching Mechanisms

We present an experimental study where we analyze three well- known matching mechanisms - the Boston, the Gale-Shapley, and the Top Trading Cycles mechanisms - in three different informational set- tings. Our experimental results are consistent with the theory, sug- gesting that the TTC mechanism outperforms both the Boston and the Gale-Shapley mechanisms in terms of efficiency and it is as suc- cessful as the Gale-Shapley mechanism regarding the proportion of truthful preference revelation, whereas manipulation is stronger un- der the Boston mechanism. In addition, even though agents are much more likely to revert to truthtelling in lack of information about the others' payooffs - ignorance may be beneficial in this context - , the TTC mechanism results less sensitive to the amount of information that participants hold. These results therefore suggest that the use of the TTC mechanism in practice is more desirable than of the others.

On the Decomposition of the Gini Coefficient: an Exact Approach, with an Illustration Using Cameroonian Data

Decomposing inequality indices across household groups or income sources is useful in estimating the contribution of each component to total inequality. This can help policy makers draw efficient policies to reduce disparities in the distribution of incomes using targeting tools. Decomposing relative inequality indices, such as the Gini coefficient, is not a simple procedure since, in many cases, the functional form of inequality indices is not additively separable in incomes. More importantly, for some of the indices on which this decomposition can be performed, the interpretation of the decomposition components is often not well founded. In this paper, we use the Shapley value as well as analytical approaches to perform the decomposition of the Gini coefficient and generalize it, in some cases, to the decomposition of other inequality indices. For the analytical approach, our aim is to extend the same interpretation, attributed to the Gini coefficient, to that of the contribution components.Equity, Inequality, Decomposition, Shapley value

Telling the Truth May Not Pay Off

We investigate the matching algorithm used by the German central clearinghouse for university admissions (ZVS) in medicine and related subjects. This mechanism consists of three procedures based on final grades from school ("Abiturbestenverfahren", "Auswahlverfahren der Hochschulen") and on waiting time ("Wartezeitverfahren"). While these procedures differ in the criteria applied for admission they all make use of priority matching. In priority matching schemes, it is not a dominant strategy for students to submit their true preferences. Thus, strategic behaviour is expected. Using the full data set of applicants, we are able to detect some amount of strategic behaviour which can lead to inefficient matching. Alternative ways to organize the market are briefly discussed.Matching, university admissions, strategic behaviour