60 research outputs found
Cooperation under Interval Uncertainty
Classification: JEL code C71Cooperative game theory;Interval uncertainty;Core;Value;Balancedness
Coalition formation and stability
This paper aims to develop, for any cooperative game, a solution notion that enjoys stability and consists of a coalition structure and an associated payoff vector derived from the Shapley value. To this end, two concepts are combined: those of strong Nash equilibrium and Aumann--Dr\`{e}ze coalitional value. In particular, we are interested in conditions ensuring that the grand coalition is the best preference for all players. Monotonicity, convexity, cohesiveness and other conditions are used to provide several theoretical results that we apply to numerical examples including real--world economic situations.Peer ReviewedPostprint (author's final draft
Coalitional Game Theory for Communication Networks: A Tutorial
Game theoretical techniques have recently become prevalent in many
engineering applications, notably in communications. With the emergence of
cooperation as a new communication paradigm, and the need for self-organizing,
decentralized, and autonomic networks, it has become imperative to seek
suitable game theoretical tools that allow to analyze and study the behavior
and interactions of the nodes in future communication networks. In this
context, this tutorial introduces the concepts of cooperative game theory,
namely coalitional games, and their potential applications in communication and
wireless networks. For this purpose, we classify coalitional games into three
categories: Canonical coalitional games, coalition formation games, and
coalitional graph games. This new classification represents an
application-oriented approach for understanding and analyzing coalitional
games. For each class of coalitional games, we present the fundamental
components, introduce the key properties, mathematical techniques, and solution
concepts, and describe the methodologies for applying these games in several
applications drawn from the state-of-the-art research in communications. In a
nutshell, this article constitutes a unified treatment of coalitional game
theory tailored to the demands of communications and network engineers.Comment: IEEE Signal Processing Magazine, Special Issue on Game Theory, to
appear, 2009. IEEE Signal Processing Magazine, Special Issue on Game Theory,
to appear, 200
Universal characterization sets for the nucleolus in balanced games
We provide a new mo dus op erandi for the computation of the nucleolus in co op-
erative games with transferable utility. Using the concept of dual game we extend
the theory of characterization sets. Dually essential and dually saturated coalitions
determine b oth the core and the nucleolus in monotonic games whenever the core
is non-empty. We show how these two sets are related with the existing charac-
terization sets. In particular we prove that if the grand coalition is vital then the
intersection of essential and dually essential coalitions forms a characterization set
itself. We conclude with a sample computation of the nucleolus of bankruptcy games
- the shortest of its kind
The Nucleolus, the Kernel, and the Bargaining Set: An Update
One of David Schmeidler’s many important contributions in his distinguished career was the introduction of the nucleolus, one of the central single-valued solution concepts in cooperative game theory. This paper is an updated survey on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set. As a first approach to these concepts, we refer the reader to the great survey by Maschler (1992); see also the relevant chapters in Peleg and Sudholter (2003). Building on the notes of four lectures on the nucleolus and the kernel delivered by one of the authors at the Hebrew University of
Jerusalem in 1999, we have updated Maschler’s survey by adding more recent contributions to the literature. Following a similar structure, we have also added a new section that covers the bargaining set.
The nucleolus has a number of desirable properties, including nonemptiness, uniqueness, core selection, and consistency. The first way to understand it is based on an egalitarian principle among coalitions. However, by going over the axioms that characterize it, what comes across as important is its connection with coalitional stability, as formalized in the notion of the core. Indeed, if one likes a single-valued version of core stability that always yields a prediction, one should consider the nucleolus as a recommendation. The kernel, which contains the nucleolus, is based on the idea of “bilateral equilibrium” for every pair of players. And the bargaining set, which contains the
kernel, checks for the credibility of objections coming from coalitions. In this paper, section 2 presents preliminaries, section 3 is devoted to the nucleolus, section 4 to the kernel, and section 5 to the bargaining set.Iñarra acknowledges research support from the Spanish Government grant ECO2015-67519-P, and
Shimomura from Grant-in-Aid for Scientific Research (A)18H03641 and (C)19K01558
A new prospect of additivity in bankruptcy problems
This paper explores additivity-like properties ful led by bankruptcy rules. Our
main result is that the unique rule satisfying an adittivity-like property is the Minimal Overlap proposed by O'Neill. We also propose some conections relative to
additivity properties in close frameworks as bargaining rules.This work is partially supported by the Institut Valencià d´Investigacions Econòmiques and the Spanish Ministerio de Educación y Ciencia under projects SEJ2007-62656 (Alcalde) and SEJ2007-64649
(Marco-Gil and Silva). Marco-Gil also acknowledges support by the Fundación Séneca of the Agencia de Ciencia y Tecnología of the Murcian Region, under project 05838/PHCS/07 (Programa de Generación Cientìfico de Excelencia)
A Dual Egalitarian Solution
In this note we introduce an egalitarian solution, called the dual egalitarian solution, that is the natural counterpart of the egalitarian solution of Dutta and Ray (1989). We prove, among others, that for a convex game the egalitarian solution coincides with the dual egalitarian solution for its dual concave game.Concave Games
A Dual Egalitarian Solution
In this note we introduce an egalitarian solution, called the dual egalitarian solution, that is the natural counterpart of the egalitarian solution of Dutta and Ray (1989).We prove, among others, that for a convex game the egalitarian solution coincides with the dual egalitarian solution for its dual concave game.cooperative games;egalitarianism;duality
Multi-Issue Allocation Games
This paper introduces a new class of transferable-utility games, called multi-issue allocation games.These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill (1982).In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate.Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (nonnegative) exact games.The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game.Finally, this run-to-the-bank rule is characterised by means of a consistency property.game theory;allocation games
An approach to a N-person cooperative games
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Josep Vives i Santa EulàliaThis work is an overview on n-person cooperative games in Game Theory, the mathematical theory of interactive decision situations characterized by a group of agents, each of whom has to make a decision based on their own preferences on the set of outcomes. These situations are called games, agents are players and decisions are strategies. By focusing on Cooperative Game Theory, we analize concepts such as coalition formation, equilibrium, stability, fairness and the most important proposed solution concepts
- …