The Monoclus of a Coalitional Game

The analysis of single-valued solution concepts for coalitional games with transferable utilities has a long tradition. Opposed to most of this literature we will not deal with solution concepts that provide payoffs to the players for the grand coalition only, but we will analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce four closely related allocation scheme rules for coalitional games. Each of these rules results in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game allows for a PMAS. The driving force behind these rules are monotonicities, which measure the payoff difference for a player between two nested coalitions. From a functional point of view these monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Two different domains and two different collections of monotonicities result in four allocation scheme rules. For each of the rules we deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues by providing a sequence of linear programs.cooperative game theory;population monotonic allocation schemes;allocation scheme rules

Axiomatizations of the Value of Matrix Games

The function that assigns to each matrix game (i.e., the mixed extension of a finite zero-sum two-player game) its value is axiomatized by a number of intuitive properties.game theory;noncooperative games;matrix games;axiomatic methods

Symmetric Convex Games and Stable Structures

We study the model of link formation that was introduced by Aumann and Myerson (1988) and focus on symmetric convex games with transferable utilities. We answer an open question in the literature by showing that in a specific symmetric convex game with six players a structure that results in the same payoffs as the full cooperation structure can be formed according to a subgame perfect Nash equilibrium.symmetric convex game;undirected graph;link formation;stable structures

Fuzzy Cores and Fuzzy Balancedness

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it satisfies all (fuzzy) balanced inequalities. We also consider deposit games to illustrate the use of the main result.Cooperative fuzzy games;fuzzy balancedness;fuzzy core

The Shapley Value for Partition Function Form Games

Different axiomatic systems for the Shapley value can be found in the literature.For games with a coalition structure, the Shapley value also has been axiomatized in several ways.In this paper, we discuss a generalization of the Shapley value to the class of partition function form games.The concepts and axioms, related to the Shapley value, have been extended and a characterization for the Shapley value has been provided.Finally, an application of the Shapley value is given.game theory

An Axiomatization of Minimal Curb Sets

Norde et al.[Games Econ.Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent.A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games.The minimal curb sets of Basu and Weibull [Econ.Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.Minimal curb set;Consistency

Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes

In this paper we present the Subtraction Algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme.As a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegative combination of minimum cost spanning tree games corresponding to 0-1 cost functions.It turns out that the Subtraction Algorithm is closely related to the famous algorithm of Kruskal for the determination of minimum cost spanning trees.For variants of the classical minimum cost spanning tree games we show that population monotonic allocation schemes do not necessarily exist.operational research;cost allocation;game theory

Characterizing properties of approximate solutions for optimization problems

optimization

A General Framework for Cooperation under Uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the cooperative games associated with these situations are totally balanced and, hence, have non-empty cores. Finally, we consider several example situations, which can be studied using this general framework.Two-stage stochastic programming;cooperative game theory;core