Cooperative Games and Solution Concepts

1997 ◽  
pp. 1-17 ◽  
Author(s):  
Imma Curiel
Keyword(s):  
Cooperative Games ◽  
Solution Concepts

The Geometry of Solution Concepts forN-Person Cooperative Games

1974 ◽  
Vol 20 (9) ◽  
pp. 1292-1299 ◽  
Author(s):  
Richard Spinetto
Keyword(s):  
Cooperative Games ◽  
Solution Concepts

scholarly journals Continuity properties of solution concepts for cooperative games

OR Spectrum ◽  
1987 ◽  
Vol 9 (2) ◽  
pp. 101-107 ◽  
Author(s):  
R. Lucchetti ◽  
F. Patrone ◽  
S. H. Tijs ◽  
A. Torre
Keyword(s):  
Cooperative Games ◽  
Solution Concepts ◽  
Continuity Properties

scholarly journals Computational Aspects of the Preference Cores of Supermodular Two-Scenario Cooperative Games

2018 ◽  
Author(s):  
Daisuke Hatano ◽  
Yuichi Yoshida
Keyword(s):  
Characteristic Function ◽  
Cooperative Games ◽  
Solution Concept ◽  
Multicast Tree ◽  
Characteristic Functions ◽  
Solution Concepts ◽  
Induced Subgraph ◽  
Computational Aspects ◽  
Tree Game ◽  
Multiple Scenarios

In a cooperative game, the utility of a coalition of players is given by the characteristic function, and the goal is to find a stable value division of the total utility to the players. In real-world applications, however, multiple scenarios could exist, each of which determines a characteristic function, and which scenario is more important is unknown. To handle such situations, the notion of multi-scenario cooperative games and several solution concepts have been proposed. However, computing the value divisions in those solution concepts is intractable in general. To resolve this issue, we focus on supermodular two-scenario cooperative games in which the number of scenarios is two and the characteristic functions are supermodular and study the computational aspects of a major solution concept called the preference core. First, we show that we can compute the value division in the preference core of a supermodular two-scenario game in polynomial time. Then, we reveal the relations among preference cores with different parameters. Finally, we provide more efficient algorithms for deciding the non-emptiness of the preference core for several specific supermodular two-scenario cooperative games such as the airport game, multicast tree game, and a special case of the generalized induced subgraph game.

Bargaining in n -person cooperative games with linearly distributed, transferable utility

1995 ◽  
Vol 451 (1942) ◽  
pp. 349-365 ◽  
Keyword(s):  
Cooperative Games ◽  
Binary Trees ◽  
Transferable Utility ◽  
Solution Concepts ◽  
Coalition Structures ◽  
Player Game ◽  
The Subject ◽  
Simply Connected

Coalitional aspects of bargaining are investigated. Binary trees describe coalition structures; at a vertex the payoffs are distributed linearly according to parameters for the two sets. The parameter for a player-set is assumed to be the sum of the parameters in that set. These values are the subject of bargaining. The criteria for the results of bargaining are formulated, thus determining a bargaining point(s) in the space R of the parameters. R can be divided into regions in which a particular tree is maximal. In completely essential 3-player games these regions are simply connected; the bargaining point is where these regions meet. The solutions for 4- and n -player games present immense problems. Our solutions are compared with other solution concepts. We show that in the 3-player game our solution is monotonic but not completely coalitionally monotonic.

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