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Performance bounds for nash equilibria in submodular utility systems with user groups

Journal of Control and Decision 2018年第1期5卷 1-18页

作者： Yajing Liu Edwin K.P.Chong Ali Pezeshki Department of Electrical and Computer Engineering Colorado State UniversityFort CollinsCOUSA Department of Electrical and Computer Engineering&Department of Mathematics Colorado State UniversityFort CollinsCOUSA

It is shown that for a valid non-cooperative utility system,if the social utility function is submodular,then any nash equilibrium achieves at least 1/2 of the optimal social utility,subject to a function-dependent additive ***,if the social utility function is nondecreasing and submodular,then any nash equilibrium achieves at least 1/(1+c)of the optimal social utility,where c is the curvature of the social utility *** this paper,we consider variations of the utility system considered by Vetta,in which users are grouped *** aim is to establish how grouping and cooperation among users affect performance *** consider two types of *** first type is from a previous paper,where each user belongs to a group of users having social ties with *** this type of utility system,each user’s strategy maximises its social group utility function,giving rise to the notion of social-aware nash *** prove that this social utility system yields to the bounding results of Vetta for non-cooperative system,thus establishing provable performance guarantees for the social-aware nash *** the second type of grouping we consider,the set of users is partitioned into l disjoint groups,where the users within a group cooperate to maximise their group utility function,giving rise to the notion of group nash *** this case,each group can be viewed as a new user with vector-valued actions,and a 1/2 bound for the performance of group nash equilibria follows from the result of *** as we show tighter bounds involving curvature can be *** defining the group curvature cki associated with group i with ki users,we show that if the social utility function is nondecreasing and submodular,then any group nash equilibrium achieves at least 1/(1+max1≤i≤l cki)of the optimal social utility,which is tighter than that for the case without *** a special case,if each user has the same action space,then we have that any g

关键词： Group nash equilibrium social-aware nash equilibrium submodularity utility system

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