Cost allocation in a bank ATM network

Bjørndal, Endre; Hamers, Herbert; Koster, Maurice

doi:10.1007/s001860400351

Cited by 15 publications

(16 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further, for n ≥ 3 it has been shown in Bjorndal et al (2004) that τ (v) = η(v) = x * with x * the single element in the core of the game given by x * n = ω n and x * i = 0, i = n. Summarizing these observations, we obtain the following relations (in case n ≥ 3)…”

Section: Atm Gamessupporting

confidence: 62%

“…. , n. Thus, all these solutions satisfy the equal split property (see Bjorndal et al 2004) meaning that the cost savings ω i obtained from the cooperation between bank i = 1, and ATM bank 1 is equally distributed between these two banks. Finally, because all dividends are nonnegative, this payoff vector also belongs to the core of the game.…”

Section: Atm Gamesmentioning

confidence: 94%

“…In this subsection we consider ATM games as introduced in Bjorndal et al (2004). An ATM-game models a situation of n banks on a single location, where some banks have an Automated Teller Machine (money dispenser) and others do not.…”

Section: Atm Gamesmentioning

confidence: 99%

“…In Bjorndal et al (2004) a single solution concept is proposed for both situations with one bank with ATM and situations with a single bank without ATM. They call this solution the aggregate allocation solution.…”

Section: Atm Gamesmentioning

confidence: 99%

See 3 more Smart Citations

Harsanyi power solutions for graph-restricted games

2010

View full text Add to dashboard Cite

We consider cooperative transferable utility games, or simply TU-games, with limited communication structure in which players can cooperate if and only if they are connected in the communication graph. Solutions for such graph games can be obtained by applying standard solutions to a modified or restricted game that takes account of the cooperation restrictions. We discuss Harsanyi solutions which distribute dividends such that the dividend shares of players in a coalition are based on power measures for nodes in corresponding communication graphs. We provide axiomatic characterizations of the Harsanyi power solutions on the class of cycle-free graph games and on the class of all graph games. Special attention is given to the Harsanyi degree solution which equals the Shapley value on the class of complete graph games and equals the position value on the class of cycle-free graph games. The Myerson value is the Harsanyi power solution that is based on the equal power measure. Finally, various applications are discussed.

show abstract

Section: Atm Gamessupporting

confidence: 62%

Section: Atm Gamesmentioning

confidence: 94%

Section: Atm Gamesmentioning

confidence: 99%

Section: Atm Gamesmentioning

confidence: 99%

See 2 more Smart Citations

Harsanyi power solutions for graph-restricted games

2010

View full text Add to dashboard Cite

show abstract

“…Applications of peer group games are, e.g. polluted river games (Ni and Wang (2007) and Dong et al (2012)), liability games (Dehez and Ferey 2013), the duals of airport games (Littlechild and Owen 1973), auction games (Graham et al 1990) and ATM games (Bjorndal et al 2004). From 24 Consider the game with permission structure (v, D) on N = {1, 2, 3} given by D = {(1, 2), (2, 3)} and v = u {3} .…”

Section: Applicationsmentioning

confidence: 99%

Games with a permission structure - A survey on generalizations and applications

Brink

2017

TOP

View full text Add to dashboard Cite

In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that arise from restricted communication and hierarchies. This survey discusses several models of hierarchy restrictions and their relation with communication restrictions. In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize existing solutions for TU-games. In this survey, we mainly focus on axiomatizations of the Shapley value in different models of games with a hierarchically structured player set, and their applications. Not only do these axiomatizations provide insight in the Shapley value for these models, but also by considering the types of axioms that characterize the Shapley value, we learn more about different network structures. A central model of games with hierarchies is that of games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players that need permission from other players before they are allowed to cooperate. This permission structure is represented by a directed graph. Generalizations of this model are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications, in particular auction games and hierarchically structured firms.This invited paper is discussed in the comments available at

show abstract

Networks, Communication and Hierarchy: Applications to Cooperative Games

Algaba

Brink

2021

Trends in Mathematics

View full text Add to dashboard Cite

Agents participating in different kind of organizations, usually take different positions in some network structure. Two well-known network structures are hierarchies and communication networks. We give an overview of the most common models of communication and hierarchy restrictions in cooperative games, compare different network structures with each other and discuss network structures that combine communication as well as hierarchical features. Throughout the survey, we illustrate these network structures by applying them to cooperative games with restricted cooperation.

show abstract

Cost allocation in a bank ATM network

Cited by 15 publications

References 10 publications

Harsanyi power solutions for graph-restricted games

Harsanyi power solutions for graph-restricted games

Games with a permission structure - A survey on generalizations and applications

Networks, Communication and Hierarchy: Applications to Cooperative Games

Contact Info

Product

Resources

About