Multiplayer Allocations in the Presence of Diminishing Marginal Contributions: Cooperative Game Analysis and Applications in Management Science

We use cooperative game theory to investigate multiplayer allocation problems under the almost diminishing marginal contributions (ADMC) property. This property indicates that a player’s marginal contribution to a non-empty coalition decreases as the size of the coalition increases. We develop ADMC games for such problems and derive a necessary and sufficient condition for the non-emptiness of the core. When the core is non-empty, at least one extreme point exists, and the maximum number of extreme points is the total number of players. The Shapley value may not be in the core, which depends on the gap of each coalition. A player can receive a higher allocation based on the Shapley value in the core than based on the nucleolus, if the gap of the player is no greater than the gap of the complementary coalition. We also investigate the least core value for ADMC games with an empty core. To illustrate the applications of our results, we analyze a code-sharing game, a group buying game, and a scheduling profit game. This paper was accepted by Chung Piaw Teo, optimization.

Bounds on the Cost of Stabilizing a Cooperative Game

A key issue in cooperative game theory is coalitional stability, usually captured by the notion of the core---the set of outcomes that are resistant to group deviations. However, some coalitional games have empty cores, and any outcome in such a game is unstable. We investigate the possibility of stabilizing a coalitional game by using subsidies. We consider scenarios where an external party that is interested in having the players work together offers a supplemental payment to the grand coalition, or, more generally, a particular coalition structure. This payment is conditional on players not deviating from this coalition structure, and may be divided among the players in any way they wish. We define the cost of stability as the minimum external payment that stabilizes the game. We provide tight bounds on the cost of stability, both for games where the coalitional values are nonnegative (profit-sharing games) and for games where the coalitional values are nonpositive (cost-sharing games), under natural assumptions on the characteristic function, such as superadditivity, anonymity, or both. We also investigate the relationship between the cost of stability and several variants of the least core. Finally, we study the computational complexity of problems related to the cost of stability, with a focus on weighted voting games.

Public library mobile apps in Scotland: views from the local authorities and the public

Purpose The purpose of this paper is to examine current public library apps in Scotland and assess Scottish public library users’ opinions of those apps. Design/methodology/approach Two qualitative and quantitative surveys were conducted. One survey was distributed to each Scottish local authority, the entities responsible for public libraries and Scotland. The second survey was made available to the public. The results were analysed with nonparametric statistics and content analysis. Findings All 32 authorities responded. In all, 17 authorities had an app, two had one in development, and 13 had none. Offering an alternative means of communication to patrons was the main reason for providing an app, while cost and low priority were the main reasons provided against app provision. Authorities were satisfied with the core services offered in their apps, but less so with others. No authorities had consulted the public regarding app provision. The public (n=185), while satisfied with current library apps, criticised the complex procedures required to access external services. Patrons from authorities without an app stated interest in apps. Research limitations/implications It is vital for public libraries to implement at least core services that are optimised for mobile devices. They should consult with the public before and throughout the development process to ensure they are happy with the implementation. Originality/value This is the first known study to explore public library app use in Scotland as well as one of the first in public library app use worldwide.

The International Criminal Court’s Libya Case(s)—The Need for Consistency with International Human Rights as to Due Process and the Death Penalty

The icc’s Libya cases raise interesting questions about the icc’s interaction with national jurisdictions that retain the death penalty. In the case against Abdullah Al-Senussi, the icc ruled he could be tried in Libya—his case was ‘inadmissible’—despite Libya retaining the death penalty and despite fair trial concerns. Yet, Rome Statute Article 21.3 directs the Court to be consistent with international human rights. Is it consistent with international human rights to indirectly authorize trial in a country that retains the death penalty, under conditions that cannot guarantee at least core due process protections? This article argues that it is not. Furthermore, this article argues that the Appeals Chamber in Senussi was insufficiently concerned with due process violation in the national jurisdiction—in a situation one could well-anticipate a former high-level regime official would not receive a fair trial post-regime change.