STABILITY AND ALLOCATION IN A THREE-PLAYER GAME

2013 ◽  
Vol 30 (03) ◽  
pp. 1340014
Author(s):  
LEQIN WU ◽  
XIN CHEN ◽  
YE LU ◽  
YA-XIANG YUAN
Keyword(s):  
Cooperative Game ◽  
Grand Coalition ◽  
Transferable Utility ◽  
Price Model ◽  
Coalition Structures ◽  
Novel Approach ◽  
Stable Coalition ◽  
Core Solution ◽  
Player Game ◽  
Stability Concept

We study a three-player cooperative game with transferable utility where the players may form different coalition structures. A new concept of stability of a coalition is introduced, and the existence of a stable coalition is proven. Based on this stability concept, a novel approach is given to determine sensible allocations in a grand coalition of three players. We also compare our result with classical core solution and implement our theory on a specific price model.

STABLE COALITION STRUCTURES UNDER RESTRICTED COALITIONAL CHANGES

2014 ◽  
Vol 16 (03) ◽  
pp. 1450006 ◽  
Author(s):  
YUKIHIKO FUNAKI ◽  
TAKEHIKO YAMATO
Keyword(s):  
Coalition Formation ◽  
Sufficient Conditions ◽  
Coalition Structure ◽  
Grand Coalition ◽  
Cournot Oligopoly ◽  
Common Pool Resource ◽  
Common Pool ◽  
Coalition Structures ◽  
Stable Coalition ◽  
Stability Concept

In this paper, we examine whether farsighted players form the efficient grand coalition structure in coalition formation games. We propose a stability concept for a coalition structure, called sequentially stability, when only bilateral mergers of two separate coalitions are feasible because of high negotiation costs. We provide an algorithm to check the sequential stability of the grand coalition structure as well as sufficient conditions for which the efficient grand coalition structure is sequentially stable. We also illustrate out results by means of common pool resource games and Cournot oligopoly games.

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.

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 Sequentially Stable Coalition Structures

2007 ◽  
Author(s):  
Yukihiko Funaki ◽  
Takehiko Yamato
Keyword(s):  
Coalition Structures ◽  
Stable Coalition

LINEAR AND INTEGER PROGRAMMING TECHNIQUES FOR COOPERATIVE GAMES

2002 ◽  
Vol 13 (05) ◽  
pp. 653-666 ◽  
Author(s):  
Qizhi Fang ◽  
Shanfeng Zhu
Keyword(s):  
Integer Programming ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Value Function ◽  
Linear Program ◽  
Grand Coalition ◽  
The Core ◽  
Programming Techniques ◽  
Theoretical Results

Let Γ = (N, v) be a cooperative game with the player set N and value function v : 2N → R. A solution of the game is in the core if no subset of players could gain advantage by breaking away from the grand coalition of all players. This paper surveys theoretical results on the cores for some cooperative game models. These results proved that the linear program duality characterization of the core is a very powerful tool. We will focus on linear and integer programming techniques applied in this area.

scholarly journals A Novel Zero-Sum Polymatrix Game Theory Bidding Strategy for Power Supply Market

2019 ◽  
Vol 8 (2) ◽  
pp. 5669-5675
Keyword(s):  
Game Theory ◽  
Financial Risk ◽  
Optimal Solution ◽  
Theoretic Approach ◽  
Bidding Strategies ◽  
Load Demand ◽  
Novel Approach ◽  
Game Theoretic ◽  
Player Game ◽  
Zero Sum

The competitive power system market involves very high financial risk due to the essential requirements of real-time bidding decision making. Decisions once taken cannot be altered easily because multiple generators participate in bidding process while simultaneously dispatching to meet the load demand most economically. In order to avoid such risks it becomes pertinent to re-structure the bidding strategies from time to time to meet upcoming techno-economical challenges. In this paper, three generating units are studied using Matrix Laboratory software with a novel approach for deciding the best strategy from the most economical strategy viewpoint. A scenario of different formulations is created for muti-player game, which then is solved with the help of zero-sum polymatrix game theory. A systematic tabular layout of revenues pertaining to each formulation in terms of mixed strategies is developed. The minimax and maximin revenues, identified using Game theoretic approach, gave the most economical strategy. Thus exact and self-enforcing generalized method for best bidding strategies of all three generators are logically derived for the most optimal solution.

The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy

2016 ◽  
Vol 18 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Frank Huettner ◽  
Harald Wiese
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Transferable Utility ◽  
Tu Game ◽  
Tu Games ◽  
Permission Value

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.

scholarly journals Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre- and Post-Brexit Context

2018 ◽  
Vol 20 (02) ◽  
pp. 1850001 ◽  
Author(s):  
Evangelos Toumasatos ◽  
Stein Ivar Steinshamn
Keyword(s):  
Coalition Formation ◽  
Net Present Value ◽  
Growth Function ◽  
The European Union ◽  
Northeast Atlantic ◽  
Atlantic Mackerel ◽  
Coalition Structures ◽  
Management Regime ◽  
Player Game ◽  
The Uk

The partition function approach is applied to study coalition formation in the Northeast Atlantic mackerel fishery in the presence of externalities. Atlantic mackerel is mainly exploited by the European Union (EU), the United Kingdom (UK), Norway, the Faroe Islands and Iceland. Two games are considered. First, a four-player game where the UK is still a member of the EU. Second, a five-player game where the UK is no longer a member of the union. Each game is modeled in two stages. In the first stage, players form coalitions following a predefined set of rules. In the second stage, given the coalition structure that has been formed, each coalition chooses the economic strategy that maximizes its own net present value of the fishery, given the behavior of the other coalitions. The game is solved using backward induction to obtain the set of Nash equilibria coalition structures in pure strategies, if any. We find that the current management regime is among the stable coalition structures in all eight scenarios of the four-player game but in only one case of the five-player game. In addition, stability in the five-player game is sensitive to the growth function applied and the magnitude of the stock elasticity parameter.

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