THE EGALITARIAN NON-k-AVERAGED CONTRIBUTION (ENkAC-) VALUE FOR TU-GAMES

1999 ◽  
Vol 01 (01) ◽  
pp. 45-61 ◽  
Author(s):  
TSUNEYUKI NAMEKATA ◽  
THEO S. H. DRIESSEN
Keyword(s):  
Solution Concept ◽  
Sufficient Condition ◽  
Individual Contribution ◽  
Transferable Utility ◽  
Tu Games ◽  
The Core ◽  
Centre Of Gravity ◽  
Transferable Utility Game ◽  
Individual Contributions ◽  
Transferable Utility Games

This paper deals in a unified way with the solution concepts for transferable utility games known as the Centre of the Imputation Set value (CIS-value), the Egalitarian Non-Pairwise-Averaged Contribution value (ENPAC-value) and the Egalitarian Non-Separable Contribution value (ENSC-value). These solutions are regarded as the egalitarian division of the surplus of the overall profits after each participant is conceded to get his individual contribution specified in a respective manner. We offer two interesting individual contributions (lower- and upper-k-averaged contribution) based on coalitions of size k(k ∈ {1,…,n-1}) and introduce a new solution concept called the Egalitarian Non-k-Averaged Contribution value ( EN k AC -value). CIS-, ENPAC- and ENSC-value are the same as EN 1 AC -, EN n-2 AC - and EN n-1 AC -value respectively. It turns out that the lower- and the upper-k-averaged contribution form a lower- and an upper-bound of the Core respectively. The Shapley value is the centre of gravity of n-1 points; EN 1 AC -,…, EN n-1 AC -value. EN k AC -value of the dual game is equal to EN n-k AC -value of the original game. We provide a sufficient condition on the transferable utility game to guarantee that the EN k AC -value coincides with the well-known solution called prenucleolus. The condition requires that the largest excesses at the EN k AC -value are attained at the k-person coalitions, whereas the excesses of k-person coalitions at the EN k AC -value do not differ.

scholarly journals THE POSITIVE PREKERNEL OF A COOPERATIVE GAME

2000 ◽  
Vol 02 (04) ◽  
pp. 287-305 ◽  
Author(s):  
PETER SUDHÖLTER ◽  
BEZALEL PELEG
Keyword(s):  
Cooperative Game ◽  
Weak Version ◽  
Transferable Utility ◽  
Bargaining Set ◽  
The Core ◽  
Reduced Game ◽  
Positive Kernel ◽  
Game Property ◽  
Transferable Utility Games

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which are both sub-solutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a sub-solution of the reactive (pre)bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by non-emptiness, anonymity, reasonableness, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.

scholarly journals The average covering tree value for directed graph games

2019 ◽  
Vol 39 (2) ◽  
pp. 315-333 ◽  
Author(s):  
Anna Khmelnitskaya ◽  
Özer Selçuk ◽  
Dolf Talman
Keyword(s):  
Directed Graph ◽  
Undirected Graph ◽  
Solution Concept ◽  
Transferable Utility ◽  
Communication Structure ◽  
Gravity Center ◽  
Dominance Relations ◽  
Graph Games ◽  
Covering Tree ◽  
Transferable Utility Games

Abstract We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.

STABILITY OF THE CORE IN A CLASS OF NTU GAMES: A CHARACTERIZATION

2002 ◽  
Vol 04 (02) ◽  
pp. 165-172 ◽  
Author(s):  
ANINDYA BHATTACHARYA ◽  
AMIT K. BISWAS
Keyword(s):  
Cooperative Games ◽  
Stable Set ◽  
Regularity Conditions ◽  
Transferable Utility ◽  
Large Core ◽  
Von Neumann ◽  
Ntu Games ◽  
The Core ◽  
Important Solution ◽  
Transferable Utility Games

The core and the stable set are possibly the two most crucially important solution concepts for cooperative games. The relation between the two has been investigated in the context of symmetric transferable utility games and this has been related to the notion of large core. In this paper the relation between the von-Neumann–Morgenstern stability of the core and the largeness of it is investigated in the case of non-transferable utility (NTU) games. The main findings are that under certain regularity conditions, if the core of an NTU game is large then it is a stable set and for symmetric NTU games the core is a stable set if and only if it is large.

scholarly journals On extensions of the core and the anticore of transferable utility games

2013 ◽  
Vol 43 (1) ◽  
pp. 37-63 ◽  
Author(s):  
Jean Derks ◽  
Hans Peters ◽  
Peter Sudhölter
Keyword(s):  
Transferable Utility ◽  
The Core ◽  
Transferable Utility Games

USING THE ASPIRATION CORE TO PREDICT COALITION FORMATION

2012 ◽  
Vol 14 (01) ◽  
pp. 1250004 ◽  
Author(s):  
CAMELIA BEJAN ◽  
JUAN CAMILO GÓMEZ
Keyword(s):  
Nash Equilibrium ◽  
Coalition Formation ◽  
Solution Concept ◽  
Transferable Utility ◽  
Tu Game ◽  
Subgame Perfect Nash Equilibrium ◽  
The Core ◽  
Core Solution ◽  
Aspiration Core ◽  
Overlapping Coalitions

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

The Competitive Solution for N-Person Games Without Transferable Utility, With an Application to Committee Games

1978 ◽  
Vol 72 (2) ◽  
pp. 599-615 ◽  
Author(s):  
Richard D. McKelvey ◽  
Peter C. Ordeshook ◽  
Mark D. Winer
Keyword(s):  
Cooperative Game Theory ◽  
Solution Concept ◽  
Transferable Utility ◽  
Bargaining Set ◽  
The Core ◽  
Spatial Games ◽  
Spatial Game ◽  
Standard Solution ◽  
Special Case ◽  
Made In

This essay defines and experimentally tests a new solution concept for n-person cooperative games—the Competitive Solution. The need for a new solution concept derives from the fact that cooperative game theory focuses for the most part on the special case of games with transferable utility, even though, as we argue here, this assumption excludes the possibility of modelling most interesting political coalition processes. For the more general case, though, standard solution concepts are inadequate either because they are undefined or they fail to exist, and even if they do exist, they focus on predicting payoffs rather than the coalitions that are likely to form.The Competitive Solution seeks to avoid these problems, but it is not unrelated to existent theory in that we can establish some relationships (see Theorems 1 and 2) between its payoff predictions and those of the core, the V-solution and the bargaining set. Additionally, owing to its definition and motivation, nontrivial coalition predictions are made in conjunction with its payoff predictions.The Competitive Solution's definition is entirely general, but a special class of games—majority rule spatial games—are used for illustrations and the experimental test reported here consists of eight plays of a 5-person spatial game that does not possess a main-simple V-solution or a bargaining set. Overall, the data conform closely to the Competitive Solution's predictions.

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