APPLICATIONS OF GAME THEORY TO ECONOMIC EQUILIBRIUM

1999 ◽  
Vol 01 (01) ◽  
pp. 1-8 ◽  
Author(s):  
GUILLERMO OWEN
Keyword(s):  
Game Theory ◽  
Shapley Value ◽  
Cooperative Games ◽  
Competitive Equilibrium ◽  
Random Variable ◽  
Market Games ◽  
The Core ◽  
Thin Markets ◽  
Shapley Values ◽  
Game Theoretic

One of the original expectations for the theory of cooperative games was that it would give us results valid for thin markets (where the number of traders is too small for an equilibrium to be reached). Over a period of years, however, it has been shown that, for market games, both the core and the Shapley values converge, in some sense, to the competitive equilibrium. Thus, the feeling arises that for large market games, the game-theoretic concepts yield nothing other than the equilibrium. In this article, we study the question of convergence of the Shapley value to the equilibrium and show that in some cases the convergence can be extremely slow. A very simple example (the "shoe" game) suggests that replacing the value by the equilibrium is in some sense akin to replacing a random variable by its mean.

scholarly journals Collusive Behavior of Bidders in English Auctions: A Cooperative Game Theoretic Analysis

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Takayuki Oishi
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Theoretic Analysis ◽  
Single Object ◽  
English Auctions ◽  
Game Theoretic Analysis ◽  
The Core ◽  
Game Theoretic

In practice, collusive bidders' rings in English auctions with a single object frequently distribute collusive gains among ring members via sequences of re-auctions called knockouts. The present paper introduces a model of sequences of knockouts under the situation in which each bidder has information on his evaluation and the order of the evaluations of all bidders for the object. The present paper examines the distributive function of sequences of knockouts from the viewpoint of cooperative game theory. Each sequence of knockouts yields an element of the core, two particular sequences yielding the Shapley value and the nucleolus respectively. The present paper highlights the sequence of knockouts yielding the nucleolus.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

Shapley-Based Analysis of the Leadership Formation in Social Networks

2019 ◽  
pp. 357-390
Author(s):  
Ivan Belik
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Real Life ◽  
Importance Measure ◽  
Theory Theory ◽  
Leadership Position ◽  
Leadership Formation ◽  
Game Theoretic ◽  
As Graph ◽  
Research Domains

The dynamic nature of networks formation requires the development of multidisciplinary methods for the effective social network analysis. The research presented in this chapter is motivated by the necessity to overcome the limitation of using analytical methods from the originally disconnected research domains. Hence, the authors present an approach based on techniques from different areas, such as graph theory, theory of algorithms, and game theory. Specifically, this chapter is based on the analysis of how an agent can move towards leadership in real-life socioeconomic networks. For the agent's importance measure, the authors employed a Shapley value concept from the area of cooperative games. Shapley value is interpreted as the node centrality that corresponds to the significance of the agent within a socioeconomic network. Employing game theoretic concept, the authors introduced an algorithmic approach that detects the potential connectivity modifications required to increase an agent's leadership position.

scholarly journals Synergy within the West African Triple Helix innovation systems as measured with game theory

2019 ◽  
Vol 1 (2) ◽  
pp. 96-114
Author(s):  
Eustache Mêgnigbêto
Keyword(s):  
Game Theory ◽  
Information Theory ◽  
Shapley Value ◽  
Triple Helix ◽  
Innovation Systems ◽  
West African ◽  
The West ◽  
Content Type ◽  
The Core ◽  
University Industry

Purpose University, industry and government relationships, known under the Triple Helix, have been studied under various aspects. The West African region and countries have been analysed with mutual information and transmission power, two information theory-based indicators. The purpose of this paper is to portray the landscape of West African Triple Helix innovation systems using three main game theory indicators (core, Shapley value and nucleolus) with the objective to measure the synergy within the selected innovation systems. Design/methodology/approach The collaboration between university, industry and government is modelled as a three-person coalitional game. Bibliographical data of selected countries were collected from Web of Science and organised according to collaboration patterns between the three actors. The characteristic functions of the games were computed, the cores plotted, the Shapley values and the nucleoli computed. Findings Either university or government has more power to create and lead to synergy; government shows solidarity towards university and industry in most of countries; and they are joined in their efforts by industry in two countries. The core exists in all the countries meaning that all the selected innovation systems present synergy; however, the extent is limited and varies over countries. Research limitations/implications Innovation includes all research products; however, this study focuses on publications only. Originality/value Synergy within a Triple Helix innovation system is studied up to now with information theory indicators. The paper portrays the landscape of West African Triple Helix innovation systems using three main game theory indicators: the core, the Shapley value and the nucleolus and gives a new way to study university, industry and government relationships.

scholarly journals Hart–Mas-Colell consistency and the core in convex games

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

AbstractThis paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

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.

scholarly journals CONVEXITY IN STOCHASTIC COOPERATIVE SITUATIONS

2005 ◽  
Vol 07 (01) ◽  
pp. 25-42 ◽  
Author(s):  
JUDITH TIMMER ◽  
PETER BORM ◽  
STEF TIJS
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Convex Game ◽  
Tu Games ◽  
New Model ◽  
The Core ◽  
Random Payoffs ◽  
Marginal Vectors

This paper introduces a new model concerning cooperative situations in which the payoffs are modeled by random variables. We analyze these situations by means of cooperative games with random payoffs. Special attention is paid to three types of convexity, namely coalitional-merge, individual-merge and marginal convexity. The relations between these types are studied and in particular, as opposed to their deterministic counterparts for TU games, we show that these three types of convexity are not equivalent. However, all types imply that the core of the game is nonempty. Sufficient conditions on the preferences are derived such that the Shapley value, defined as the average of the marginal vectors, is an element of the core of a convex game.

scholarly journals Covid-19 meets game theory: a proposed experiment

2021 ◽  
Author(s):  
Giorgos Stamatopoulos
Keyword(s):  
Shapley Value ◽  
Relative Weight ◽  
Theoretic Model ◽  
Marginal Contribution ◽  
Combination Theory ◽  
Shapley Values ◽  
Game Theoretic ◽  
Practical Level ◽  
Bliss Independence

Abstract Researchers around the globe are searching for a "combo-drug" against Covid-19 by trying to combine various existing drugs. Given a set of such drugs, various algorithms (based, for example, on artificial intelligence) are used to identify the efficacy of different shares of the constituent drugs in the combo-drug. Namely, the relative weight of each drug in a "cooperative" scheme of therapy is sought-after. In the current note we propose to identify these weights using the theory of cooperative games, and in particular the Shapley value, one of the fundamental solution concepts of such games. We derive the weight of each drug by its (normalized) average marginal contribution over all possible "coalitions" of drugs it is used with, where a drug's marginal contribution to a coalition is defined as the increase in the coalition's probability to act against a virus should the drug become its "member". Hence we endow each drug with a consistent measure of significance (which is due to the consistency that Shapley value is associated with). At a theoretical level, we build the cooperative game, and compute the Shapley values, within a milestone model in drug combination theory, the Bliss independence model. At a practical level, the predictions of our game-theoretic model can be tested by using in-vitro experiments, namely experiments that are conducted in test tubes.

scholarly journals Joining insured groups: how to split the emerging profit

2017 ◽  
Vol 8 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Elinor Mualem ◽  
Abraham Zaks
Keyword(s):  
Game Theory ◽  
Risk Factor ◽  
Standard Deviation ◽  
Cooperative Games ◽  
Utility Functions ◽  
Single Group ◽  
Total Risk ◽  
Insurance Plan ◽  
Shapley Values

In the process of evaluating the premium of an insurance plan, one considers the risk arising from various uncertainties. The authors suppose for a plan whose net premium is p and the standard deviation is σ the premium including the risk factor will be p + 3σ for a given member, and 3σ reflects the risk. For a group of n members with the same premium p and with standard deviation σ, the premium including the risk factor will be p + 3σ/√n where 3σ/√n reflects the risk for each member of the group. The authors study the emerging profit in case of n insured groups each with its own premium and its own risk when all the n insured groups merge into a single group uniting all insured members. They prove that there emerge a profit due to joining the n groups into a single one due to a reduced total risk of the n separate insured groups when merging into a single group. The emerging profit between the various groups may be divided using the Shapley values method or using utility functions for each group. The auhors discuss various reasonable ways to split the emerging profit between the n groups and show that the split of the profit depends on the chosen method. The main tools are techniques of game theory, in particular those of cooperative games.

scholarly journals Allocation of Environmental Impacts in Circular and Cascade Use of Resources—Incentive-Driven Allocation as a Prerequisite for Cascade Persistence

2020 ◽  
Vol 12 (11) ◽  
pp. 4366
Author(s):  
Max Rehberger ◽  
Michael Hiete
Keyword(s):  
Environmental Impacts ◽  
Shapley Value ◽  
Theoretic Approach ◽  
The Core ◽  
Use Of Resources ◽  
The Shapley Value ◽  
Game Theoretic ◽  
Set Up ◽  
Generic Set

In cascade use, a resource is used consecutively in different application areas demanding less and less quality. As this practically allows using the same resource several times, cascading contributes to resource efficiency and a circular economy and, therefore, has gained interest recently. To assess the advantages of cascading and to distribute the environmental impacts arising from resource extraction/processing, potentially needed treatment and upcycling within the cascade chain and end-of-life proesses represent a difficult task within life cycle assessment and highlight the needs for a widely applicable and acceptable framework of how to allocate the impacts. To get insight into how the allocation is handled in cascades, a systematic literature review was carried out. Starting from this status quo, common allocation approaches were extracted, harmonized, and evaluated for which a generic set of criteria was deduced from the literature. Most importantly, participants must be willing to set up a cascade, which requires that for each participant, there are individual benefits, e.g., getting less environmental burdens allocated than if not joining. A game-theoretic approach based on the concept of the core and the Shapley value was presented, and the approaches were benchmarked against this in a case-study setting. Several of the approaches laid outside the core, i.e., they did not give an incentive to the participants to join the cascade in the case study. Their application for cascade use is, therefore, debatable. The core was identified as an approach for identifying suitable allocation procedures for a problem at hand, and the Shapley value identified as a slightly more complex but fair allocation procedure.

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