Model of Cooperative Games with Coalition Structures on the Cost Sharing Scheme of Installing Elevators for Existing Multi-storey Residential Buildings and Its Axiomatization
A cooperative game with transferable utility(TU-game)assumes that all players can communicate with one another and focus on how to rationalize the distribution of group benefits.TU-game assumes that all possible coalitions are feasible in the classical TU-game.In practice,however,many collaborations do not really happen due to geographical,communication technology or organizational influences.We therefore need to place limits on cooperation,and there are two main types of constraint structures in cooperative games.Myerson(1977)intro-duced restrictions to the communication among players through a graph,and claimed that players can cooperate only when there is a link between them.Aumann(1974)constructed a cooperative game with coalition struc-tures,and declared that only players belong to a same priori union can they communicate.Usually,we call the allocation in a cooperative game the value.The Shapley value(Shapley,1953)is the most famous value in TU-game,claiming that benefits should be distributed according to marginal utility.However,the equal division value divides the benefits equally,and believes that equal distribution makes cooperation possible.China built a large number of multi-storey buildings from the 1970s to 1980s,and due to technical and financial pressures,most of them were not fitted with elevators.In order to improve the quality of life of the resi-dents and solve thetravel difficulties of the elderly,governments accelerate the process of installing elevators in existing multi-storey residential buildings.There are many factors that affect the installation work,and the most controversial one is the cost sharing scheme.Because the residents on different floors have different demands for elevators,the residents on lower floors often do not agree to install elevators or share a lot of costs,which has seriously delayed the progress of installing elevators.Therefore,this paper proposes a weight system to describe this demand difference,or named allocation difference.Considering the cooperative game with coalition struc-tures,as residents on the same floor often have the same interests,we take the residents on the same floor as a priori union.In this way,the problem with installing elevators in existing multi-storey residential buildings can be reduced to a weighted cooperative game model with coalition structures.Based on this model,this paper proposes an allocation method called"weighted division value".We use the four properties of additivity,weighted symmetry within unions,weighted symmetry among unions and nullif-ying player property to characterize this value.Then we apply this value to the cost sharing scheme of installing elevators in existing multi-storey residential buildings in Shanghai.When the appropriate weights are taken,the allocation rule implies the guiding standard for cost sharing of owners in existing multi-storey residential buildings in most cities of China,which provides an accurate theoretical basis for the perfection,promotion and implemen-tation of this standard.The results show that residents on lower floors will share less under a staggered entry and those on higher floors will share less under a flat entry,which explains the reason for disputes among residents over different methods of installation.And if we only use floorage as the basis for determining weights,there will also be a large cost difference between residents on the same floor,which is likely to undermine the original union structure.Finally,the"weighted distribution value"proposed in this paper can also be used in the alloca-tion of enterprise performance bonus,stock dividend and other construction costs of facilities(wells,monitoring,fitness equipment).
cooperative gameallocation rulecoalition structureweighted distribution valueexisting multi-storey residential buildinginstall elevator
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