scholarly journals Nonadditive integration and some solutions of cooperative games

2021 ◽  
Vol 13 (1) ◽  
pp. 5-27
Author(s):  
Валерий Александрович Васильев ◽  
Valery Vasil'ev
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Support Function ◽  
Cooperative Game Theory ◽  
Measurable Space ◽  
Symmetric Power ◽  
Infinite Games ◽  
The Core ◽  
Universal Approach ◽  
Set Function

In the paper, we propose three schemes of nonadditive integration based on several extensions of nonadditive set function and integrand to the appropriate symmetric power of the original measurable space. A survey on the integral representation of some classic objects of the cooperative game theory, derived by nonadditive integration, is given. A universal approach for investigation of both finite and infinite games is developed. We pay a particular attention to the Shapley value, Owen multilinear extension, and support function of the core of a convex cooperative game.

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 The core and superdifferential of a fuzzy TU-cooperative game

2020 ◽  
Vol 12 (2) ◽  
pp. 20-35
Author(s):  
Валерий Александрович Васильев ◽  
Valery Vasil'ev
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Subdifferential Calculus ◽  
The Core ◽  
Side Payments ◽  
Weak Homogeneity ◽  
Fuzzy Game

In the paper, we consider conditions providing coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that one of the most simple sufficient conditions consists of weak homogeneity. Moreover, by applying so-called S*-representation of a fuzzy game introduced by the author, we show that for any vwith nonempty core C(v) there exists some game u such that C(v) coincides with the superdifferential of u. By applying subdifferential calculus we describe a structure of the core forboth classic fuzzy extensions of the ordinary cooperative game (e.g., Aubin and Owen extensions) and for some new continuations, like Harsanyi extensions and generalized Airport game.

scholarly journals Cooperative Games with Overlapping Coalitions

2010 ◽  
Vol 39 ◽  
pp. 179-216 ◽  
Author(s):  
G. Chalkiadakis ◽  
E. Elkind ◽  
E. Markakis ◽  
M. Polukarov ◽  
N. R. Jennings
Keyword(s):  
Coalition Formation ◽  
Cooperative Games ◽  
Cooperative Game Theory ◽  
Coalition Structure ◽  
Coalitional Games ◽  
The Core ◽  
Coalition Structures ◽  
Coalition Formation Process ◽  
The Social ◽  
Overlapping Coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.

Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions

2019 ◽  
Vol 7 (1) ◽  
pp. 1-16
Author(s):  
Cui Liu ◽  
Hongwei Gao ◽  
Ovanes Petrosian ◽  
Juan Xue ◽  
Lei Wang
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Games ◽  
Characteristic Functions ◽  
The Core ◽  
The Shapley Value ◽  
Irrational Behavior ◽  
The Individual

Abstract Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.

On Inheritance of Complementarity in Non-Additive Measures Under Bounded Interactions

2018 ◽  
Vol 22 (1) ◽  
pp. 27-33
Author(s):  
Katsushige Fujimoto ◽  
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Cooperative Game Theory ◽  
Multicriteria Decision Making ◽  
Multicriteria Decision ◽  
Restricted Domains ◽  
Additive Measures ◽  
Exponential Complexity

The notions ofk-monotonicity and superadditivity for non-additive measures (e.g., capacity and cooperative games) are used as indices to measure the complementarity of criteria/coalitions in decision-making involving multiple criteria and/or cooperative game theory. To avoid exponential complexity in capacity-based multicriteria decision-making models,k-additive capacities and/or 𝒞-decomposable capacities are often adopted. While, in cooperative game theory, under communication-restricted situations, some coalitions cannot generally be formed. This paper investigates the inheritance of complementary relationships/effects in non-additive measures with restricted domains (or under bounded interactions).

SOCIAL CHOICE AND COOPERATIVE GAME THEORY: VOTING GAMES AS SOCIAL AGGREGATION FUNCTIONS

2013 ◽  
Vol 15 (03) ◽  
pp. 1340012 ◽  
Author(s):  
MATHIEU MARTIN ◽  
MAURICE SALLES
Keyword(s):  
Game Theory ◽  
Social Choice ◽  
Cooperative Game ◽  
Topological Structure ◽  
Cooperative Game Theory ◽  
The Core ◽  
Individual Preferences ◽  
Voting Games ◽  
Aggregation Functions ◽  
Positive Results

We consider voting games as procedures to aggregate individual preferences. We survey positive results on the nonemptiness of the core of voting games and explore other solutions concepts that are basic supersets of the core such as Rubinstein's stability set and two types of uncovered sets. We consider cases where the sets of alternatives are 'ordinary' sets, finite sets and infinite sets with possibly a topological structure.

Cooperative games and multiagent systems

2013 ◽  
Vol 28 (4) ◽  
pp. 381-424 ◽  
Author(s):  
Stéphane Airiau
Keyword(s):  
Game Theory ◽  
Sensor Networks ◽  
Web Services ◽  
Multiagent Systems ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Cooperative Game Theory ◽  
Coalitional Games ◽  
Electronic Marketplaces ◽  
Key Issues

AbstractForming coalitions is a generic means for cooperation: people, robots, web services, resources, firms; they can all improve their performance by joining forces. The use of coalitions has been successful in domains such as task allocations, sensor networks, and electronic marketplaces. Forming efficient coalitions requires the identification of matching synergies between different entities (finding complementary partners, or similar partners, or partners who add diversity). In addition, the different parties must negotiate a fair repartition of the worth created by the coalition. The first part of this paper is a tutorial on cooperative game theory (also called coalitional games). We then survey the different scenarios and the key issues addressed by the multiagent systems community.

scholarly journals A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

SERIEs ◽  
2021 ◽  
Author(s):  
Gustavo Bergantiños ◽  
Juan Vidal-Puga
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Operations Research ◽  
Cooperative Games ◽  
Spanning Tree ◽  
Cooperative Game Theory ◽  
Minimum Cost ◽  
Research Literature ◽  
Minimal Tree ◽  
Connection Cost

AbstractMinimum-cost spanning tree problems are well-known problems in the operations research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory. We also relate the rules defined through cooperative games with rules defined directly from the problem, either through algorithms for computing a minimal tree, either through a cone-wise decomposition.

scholarly journals M&A Cooperative Games

Equilibrium ◽  
2014 ◽  
Vol 9 (1) ◽  
pp. 119-130
Author(s):  
Maria A. Nastych
Keyword(s):  
Game Theory ◽  
Corporate Finance ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Strategic Alliance ◽  
Cooperative Game Theory ◽  
Research Issues

Cooperative game theory instruments application to the corporate finance M&A research issues provide an ability to extend the field considered and conclusions obtained. The paper presents the M&A cooperative games modeling and its empirical implementation to analyze the airline strategic alliance as M&A deal.

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