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).

scholarly journals MODIFICATION OF SHAPLEY VALUE AND ITS IMPLEMENTATION IN DECISION MAKING

2017 ◽  
Vol 9 (1) ◽  
pp. 257-272
Author(s):  
Leszek Zaremba ◽  
Cezary S. Zaremba ◽  
Marek Suchenek
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Computer Program ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Point Of View ◽  
Practical Point ◽  
Actual Strength

Abstract The article presents a solution of a problem that is critical from a practical point of view: how to share a higher than usual discount of $10 million among 5 importers. The discount is a result of forming a coalition by 5 current, formerly competing, importers. The use of Shapley value as a concept for co-operative games yielded a solution that was satisfactory for 4 lesser importers and not satisfactory for the biggest importer. Appropriate modification of Shapley value presented in this article allowed to identify appropriate distribution of the saved purchase amount, which according to each player accurately reflects their actual strength and position on the importer market. A computer program was used in order to make appropriate calculations for 325 permutations of all possible coalitions. In the last chapter of this paper, we recognize the lasting contributions of Lloyd Shapley to the cooperative game theory, commemorating his recent (March 12, 2016) descent from this world.

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.

CORES OF STOCHASTIC COOPERATIVE GAMES WITH STOCHASTIC ORDERS

2002 ◽  
Vol 04 (03) ◽  
pp. 265-280 ◽  
Author(s):  
F. R. FERNÁNDEZ ◽  
J. PUERTO ◽  
M. J. ZAFRA
Keyword(s):  
Game Theory ◽  
Probability Distribution ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Stochastic Games ◽  
Cooperative Game Theory ◽  
Random Variables ◽  
Stochastic Orders ◽  
Core Conditions

In this paper we analyze cooperative games where the worth of a coalition is uncertain and the players only know their probability distribution. The novelty of our analysis is that the comparison among the uncertain values is done by stochastic orders among random variables. Thus, the classical concepts in cooperative game theory have to be revisited and redefined. This form of comparison leads to two-different notions of core. Conditions are given under which these cores are nonempty. The results are applied on three families of stochastic games.

scholarly journals How to Form Winning Coalitions in Mixed Human-Computer Settings

2017 ◽  
Author(s):  
Yair Zick ◽  
Kobi Gal ◽  
Yoram Bachrach ◽  
Moshe Mash
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Real World ◽  
Cooperative Games ◽  
Cooperative Game Theory ◽  
Predictive Analytics ◽  
Acceptance Rate ◽  
Good Prediction ◽  
Weighted Voting ◽  
Negotiation Game

Despite the prevalence of weighted voting in the real world, there has been relatively little work studying real people's behavior in such settings. This paper proposes a new negotiation game, based on the weighted voting paradigm in cooperative games, where players need to form coalitions and agree on how to share the gains. We show that solution concepts from cooperative game theory (in particular, an extension of the Deegan-Packel Index) provide a good prediction of people's decisions to join a given coalition. With this insight in mind, we design an agent that combines predictive analytics with decision theory to make offers to people in the game. We show that the agent was able to obtain higher shares from coalitions than did people playing other people, without reducing the acceptance rate of its offers. These results demonstrate the potential of incorporating concepts from cooperative game theory in the design of negotiating agents.

scholarly journals Compromise in cooperative game and the VIKOR method

2009 ◽  
Vol 19 (2) ◽  
pp. 225-238 ◽  
Author(s):  
Serafim Opricovic
Keyword(s):  
Game Theory ◽  
Conflict Resolution ◽  
Cooperative Game ◽  
Cooperative Game Theory ◽  
Multicriteria Decision Making ◽  
Vikor Method ◽  
Compromise Value ◽  
Transferable Utility Game ◽  
Conflicting Objectives ◽  
Decision Making Problem

Five approaches in conflict resolution are distinguished, based on cooperativeness and aggressiveness in resolving conflict. Compromise based on cooperativeness is emphasized here as a solution in conflict resolution. Cooperative game theory oriented towards aiding the conflict resolution is considered and the compromise value for TU(transferable utility)-game is presented. The method VIKOR could be applied to determine compromise solution of a multicriteria decision making problem with noncommensurable and conflicting criteria. Compromise is considered as an intermediate state between conflicting objectives or criteria reached by mutual concession. The applicability of the cooperative game theory and the VIKOR method for conflict resolution is illustrated.

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