Relaxed voting and competitive location on trees under monotonous gain functions
نویسندگان
چکیده
We examine problems of placing facilities in a tree graph to serve customers. The decision of placement is driven by an election process amongst the users, where the user preference is modeled by distances in the tree. Relaxed user preferences introduce a tolerance of users against small di erences in distances. Monotonous gain functions are introduced to provide general results of which well known problems including Simpson, security, Stackelberg and Nash are special cases.
منابع مشابه
A Linear Time Algorithm for Absolute Optima under Monotonous Gain Functions on Trees
We examine problems of placing facilities in a tree graph to serve customers. The decision of placement is driven by an election process amongst the users, where the user preference is modeled by distances in the tree. Relaxed user preferences introduce a tolerance of users against small di erences in distances. Monotonous gain functions are a natural generalization of well known competitive an...
متن کاملSpecial Issue on Optimization in Supply Chain Management Competitive location under proportional choice: 1-suboptimal points on networks
This paper is concerned with a competitive or voting location problem on networks under a proportional choice rule that has previously been introduced by Bauer et al. (1993). We refine a discretization result of the authors by proving convexity and concavity properties of related expected payoff functions. Furthermore, we answer the long time open question whether 1-suboptimal points are always...
متن کاملRelaxed ISS Small-Gain Theorems for Discrete-Time Systems
In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of exponentially ISS systems we are able to prove that the proposed relaxed small-gain theorems are non-conservative in a sense to be made precise. The proofs of the small...
متن کاملParadoxes of Multiple Elections: An Approximation Approach
When agents need to make decisions on multiple issues, applying common voting rules becomes computationally hard due to the exponentially large number of alternatives. One computationally efficient solution is to vote on the issues sequentially. In this paper, we investigate how well the winner under the sequential voting process approximates the winners under some common voting rules that admi...
متن کاملUpper Bounds for Objective Functions of Discrete Competitive Facility Location Problems
Under study is the problem of locating facilities when two competing companies successively open their facilities. Each client chooses an open facility according to his own preferences and return interests to the leader firm or to the follower firm. The problem is to locate the leader firm so as to realize the maximum profit (gain) subject to the responses of the follower company and the availa...
متن کامل