A Class of Social-Shapley Values of Cooperative Games with Graph Structure

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.

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APPLICATIONS OF GAME THEORY TO ECONOMIC EQUILIBRIUM

International Game Theory Review ◽

10.1142/s0219198999000025 ◽

1999 ◽

Vol 01 (01) ◽

pp. 1-8 ◽

Cited By ~ 2

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.

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An approach to computing interval-valued discounted Shapley values for a class of cooperative games under interval data

International Journal of General Systems ◽

10.1080/03081079.2018.1523903 ◽

2018 ◽

Vol 47 (8) ◽

pp. 794-808 ◽

Cited By ~ 3

Author(s):

Wei Fei ◽

Deng-Feng Li ◽

Yin-Fang Ye

Keyword(s):

Cooperative Games ◽

Interval Data ◽

Shapley Values ◽

Interval Valued

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Un modello cooperativo di gestione intermunicipale della raccolta differenziata dei rifiuti: un'applicazione del valore di Shapley

ECONOMICS AND POLICY OF ENERGY AND THE ENVIRONMENT ◽

10.3280/efe2008-003002 ◽

2009 ◽

pp. 19-35

Author(s):

Vitoantonio Bevilacqua ◽

Francesca Intini ◽

Silvana Kuhtz

Keyword(s):

Cooperative Games ◽

Cost Allocation ◽

Cost Effective ◽

Quantitative Information ◽

Waste Collection ◽

Single Operator ◽

Shapley Values ◽

The Individual ◽

The Cost ◽

Transferable Utility Games

- In this work we have carried out a study in order to estimate and allocate the costs related to separate waste collection in an inter-municipal area located in the province of Bari (Italy). This analysis promotes the cooperation among municipalities to manage, in an optimal way, the waste collection service. Indeed, according to Italian laws, the municipalities are responsible for organizing the management of municipal waste in accordance with principles of transparency, efficiency, effectiveness and inexpensiveness. For this reason we have built a model of separate waste collection management, highlighting the different cost functions. The total cost of the service has been divided among the individual municipalities using the theory of cooperative games, stressing that local authorities are not interested in paying off more than they would pay if they organized independently. To achieve this goal, we have created a model of aggregation of quantitative information on equipments and specialized personnel (and their costs). The problem of the cost allocation is interpreted as an example of transferable utility games and it is resolved with the technique of Shapley values that are included in the nucleolus of the inter-municipal game. Therefore it is more cost-effective to entrust a single operator with the waste collection for each area or sub domain in order not to double service costs. This work on waste management can integrate the studies and applications of the theory of cooperative games in the environmental field.Key words: Separate waste collection, Shapley values, cost allocation.JEL classifications: Q53.Parole chiave: Raccolta differenziata, valore di Shapley, allocazione dei costi.

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