Bounds for Owen's Multilinear Extension

Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.

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Minimal winning coalitions and orders of criticality

Annals of Operations Research ◽

10.1007/s10479-021-04199-6 ◽

2021 ◽

Author(s):

Michele Aleandri ◽

Marco Dall’Aglio ◽

Vito Fragnelli ◽

Stefano Moretti

Keyword(s):

Simple Game ◽

Simple Games ◽

Hitting Sets ◽

The Family ◽

Minimal Winning Coalitions ◽

Minimal Blocking

AbstractIn this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.

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The Conceptual Framework of Game Theory and Presentation of Some Simple Games

Game Theory Approach to Managerial Strategies and Value Creation ◽

10.1002/9781119419761.app1 ◽

2017 ◽

pp. 203-229

Keyword(s):

Game Theory ◽

Conceptual Framework ◽

Simple Games

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NEW APPORTIONMENT METHODS USING SIMPLE GAMES

International Game Theory Review ◽

10.1142/s0219198910002623 ◽

2010 ◽

Vol 12 (03) ◽

pp. 211-222

Author(s):

EVAN SHELLSHEAR

Keyword(s):

Simple Game ◽

Simple Games ◽

New Methods ◽

Apportionment Methods

This paper investigates the suitability of new apportionment methods based on the idea of preserving the coalition function of the simple game generated by the populations of the states of some country. The new methods fill a gap in the literature concerning apportionment methods based on winning coalitions. The main results in this paper show that the new apportionment methods do not satisfy desirable properties such as house monotonicity, quota, etc.

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A Note on the Owen Value for Glove Games

International Game Theory Review ◽

10.1142/s0219198915500140 ◽

2015 ◽

Vol 17 (04) ◽

pp. 1550014 ◽

Cited By ~ 1

Author(s):

Julia Belau

Keyword(s):

Shapley Value ◽

Simple Game ◽

Computational Effort ◽

Computationally Efficient ◽

Owen Value ◽

Allocation Rules ◽

The Shapley Value ◽

Minimal Winning Coalitions

A well-known and simple game to model markets is the glove game where worth is produced by building matching pairs. For glove games, different concepts, like the Shapley value, the component restricted Shapley value or the Owen value, yield different distributions of worth. While the Shapley value does not distinguish between productive and unproductive agents in the market and the component restricted Shapley value does not consider imbalancedness of the market, the Owen value accounts for both. As computational effort for Shapley-based allocation rules is generally high, this note provides a computationally efficient formula for the Owen value (and the component restricted Shapley value) for glove games in case of minimal winning coalitions. A comparison of the efficient formulas highlights the above-mentioned differences.

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Game theory application in marketing of innovation activity at industrial enterprises

MATEC Web of Conferences ◽

10.1051/matecconf/202031102013 ◽

2020 ◽

Vol 311 ◽

pp. 02013

Author(s):

Alexander Samoldin

Keyword(s):

Game Theory ◽

Marketing Strategy ◽

Service Sector ◽

Simple Game ◽

Optimal Choice ◽

Innovation Activity ◽

Industrial Enterprises ◽

Innovative Products ◽

Theory Application ◽

External Conditions

The theoretical game approach to analyzing marketing objectives in innovation activity is a reasonable supplement to the traditional methods and models of managing enterprises>’ marketing. The optimal choice of innovative products is significantly more important for industrial enterprises as unlike the commerce and service sector there are more expenses on the development and production of innovative products. Relatively simple game models allow checking the choice of a marketing strategy for various external conditions.

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The transients arising from the addition of heat to a gas flow

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100027894 ◽

1952 ◽

Vol 48 (3) ◽

pp. 482-498 ◽

Cited By ~ 4

Author(s):

P. M. Stocker

Keyword(s):

Gas Flow ◽

Practical Interest ◽

Theoretical Interest

Problems involving the addition of heat to a flowing gas have received considerable attention in recent years. The practical interest lies in the application to ram jets and similar engines, and the presence of entropy gradients makes the problem of theoretical interest.

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Perfect or Bounded Rationality?

Analyse & Kritik ◽

10.1515/auk-2004-0203 ◽

2004 ◽

Vol 26 (2) ◽

Cited By ~ 5

Author(s):

Werner Güth

Keyword(s):

Game Theory ◽

Simple Game ◽

Explanatory Power ◽

Economic Behavior ◽

Social Phenomena ◽

Classical Economics ◽

Experimental Game ◽

New Synthesis ◽

Experimental Game Theory ◽

Reward Allocation

AbstractSimple game experiments of the reward allocation, dictator and ultimatum type are used to demonstrate that true explanations of social phenomena cannot conceivably be derived in terms of the perfect rationality concept underlying neo-classical economics. We explore in some depth, if speculatively, how experimental game theory might bring us closer to a new synthesis or at least the nucleus of a general theory of ‘games and boundedly rational economic behavior’ with enhanced explanatory power.

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BUILDING UP SCHEDULES IN MULTIPROJECT DESIGN MANAGEMENT SYSTEMS

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MANAGEMENT COMPUTER SCIENCE AND INFORMATICS ◽

10.24143/2072-9502-2021-3-105-114 ◽

2021 ◽

Vol 2021 (3) ◽

pp. 105-114

Author(s):

Alexey Sergeyevich Dobrynin ◽

Stanislav Matveevich Kulakov ◽

Alexander Sergeyevich Koynov

Keyword(s):

Game Theory ◽

Graph Theory ◽

Discrete Optimization ◽

Systems Analysis ◽

Practical Interest ◽

Project Planning ◽

Management Systems ◽

Design Management ◽

Mathematical Apparatus ◽

New Generation

The article focuses on the problem of algorithmizing the process of building schedules in various spheres of human activity by using the modern mathematical apparatus, as well as achievements in the field of systems analysis, game theory, and graph theory. Nowadays, there have been analyzed and determined the boundaries of the effective application of many well-known heuristic and metaheuristic algorithms, which have shown good results in practice. However, despite the achievements in the discrete optimization, scheduling and network planning, the new problems of drawing up so-called coordinated schedules in the field of multi-project planning, which take into account the preferences (requests, wishes) of specific schedule executors, are still of practical interest. There have been considered the approaches and main stages of solving the problems of constructing coordinated schedules in multi-project planning, which is relevant for the development of new generation software and tools

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An issue based power index

International Journal of Game Theory ◽

10.1007/s00182-020-00737-x ◽

2020 ◽

Author(s):

Qianqian Kong ◽

Hans Peters

Keyword(s):

Linear Order ◽

Power Index ◽

Simple Game ◽

Power Indices ◽

Weighted Sum ◽

Simple Games ◽

Linear Orders ◽

Transfer Property ◽

Power Change ◽

Equal Power

Abstract An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum up to one. We consider a class of power indices, characterized by weight vectors on the set of issues. A power index in this class assigns to each player the weighted sum of the issues for which that player is pivotal. A player is pivotal for an issue if that player is a pivotal player in the coalition consisting of all players preceding that player in the linear order associated with that issue. We present several axiomatic characterizations of this class of power indices. The first characterization is based on two axioms: one says how power depends on the issues under consideration (Issue Dependence), and the other one concerns the consequences, for power, of splitting players into several new players (no advantageous splitting). The second characterization uses a stronger version of Issue Dependence, and an axiom about symmetric players (Invariance with respect to Symmetric Players). The third characterization is based on a variation on the transfer property for values of simple games (Equal Power Change), besides Invariance with respect to Symmetric Players and another version of Issue Dependence. Finally, we discuss how an issue profile may arise from preferences of players about issues.

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