Cost allocation in shortest path games

A class of cooperative games arising from shortest path problems is dened These shortest path games are shown to be totally balanced and allow a population monotonic allocation scheme Possible methods for obtaining core elements are indicated rst by relating to the allocation rules in taxation and bankruptcy problems second by constructing an explicit rule that takes opportunity costs into account by considering the costs of the second best alternative and that rewards players who are crucial to the construction of the shortest path Finally noncooperative games arising from shortest path problems are introduced in which players make bids or claims on paths The core allocations of the cooperative shortest path game coincide with the payo vectors in the strong Nash equilibria of the associated noncooperative shortest path gam

Cost allocation in connection and conflict problems on networks: a cooperative game theoretic approach

This thesis examines settings where multiple decision makers with conflicting interests benefit from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in joint single-source shortest path problems and joint weighted minimum colouring problems. The primary focus of the thesis are problems where each agent corresponds to a vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the shortest paths from the supplier to all other vertices in the graph. The optimal solution is a shortest path tree of the graph and the aim is to allocate the cost of this shortest path tree amongst the agents. The thesis defines shortest path tree problems, proposes allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core allocations for shortest path tree games are introduced and polyhedral properties of the core are studied. Moreover, computational results on finding the core and the nucleolus of shortest path tree games for the application of cost allocation in Wireless Multihop Networks are presented. The secondary focus of the thesis are problems where each agent is interested in having access to a number of facilities but can be in conflict with other agents. If two agents are in conflict, then they should have access to disjoint sets of facilities. The aim is to allocate the cost of the minimum number of facilities required by the agents amongst them. The thesis models these cost allocation problems as a class of cooperative games called weighted minimum colouring games, and characterises total balancedness and submodularity of this class of games using the properties of the underlying graph

Network Connectivity Game

We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point

Resource allocation for massively multiplayer online games using fuzzy linear assignment technique

This paper investigates the possible use of fuzzy system and Linear Assignment Problem (LAP) for resource allocation for Massively Multiplayer Online Games (MMOGs). Due to the limitation of design capacity of such complex MMOGs, resources available in the game cannot be unlimited. Resources in this context refer to items used to support the game play and activities in the MMOGs, also known as in-game resources. As for network resources, it is also one of the important research areas for MMOGs due to the increasing number of players. One of the main objectives is to ensure the Quality of Service (QoS) in the MMOGs environment for each player. Regardless, which context the resource is defined, the proposed method can still be used. Simulated results based on the network resources to ensure QoS shows that the proposed method could be an alternative

Cost Sharing Models in Game Theory = Költségelosztási modellek a játékelméletben

In our thesis we examined economic situations modeled with rooted trees and directed, acyclic graphs. In the presented problems the collaboration of economic agents (players) incurred costs or created a profit, and we have sought answers to the question of \fairly" distributing this common cost or profit. We have formulated properties and axioms describing our expecta- tions of a \fair" allocation. We have utilized cooperative game theoretical methods for modeling. After the introduction, in Chapter 2 we analyzed a real-life problem and its possible solutions. These solution proposals, namely the average cost- sharing rule, the serial cost sharing rule, and the restricted average cost- sharing rule have been introduced by Aadland and Kolpin (2004). We have also presented two further water management problems that arose during the planning of the economic development of Tennessee Valley, and discussed solution proposals for them as well (Straffinn and Heaney, 1981). We analyzed if these allocations satisfied the properties we associated with the notion of \fairness". In Chapter 3 we introduced the fundamental notions and concepts of cooperative game theory. We defined the core (Shapley, 1955; Gillies, 1959) and the Shapley value (Shapley, 1953), that play an important role in finding a \fair" allocation. In Chapter 4 we presented the class of fixed-tree game and relevant ap- plications from the domain of water management. In Chapter 5 we discussed the classes of airport and irrigation games, and the characterizations of these classes. We extended the results of Dubey (1982) and Moulin and Shenker (1992) on axiomatization of the Shapley value on the class of airport games to the class of irrigation games. We have \translated" the axioms used in cost allocation literature to the axioms corresponding to TU games, thereby providing two new versions of the results of Shapley (1953) and Young (1985). In Chapter 6 we introduced the upstream responsibility games and char- acterized the game class. We have shown that Shapley's and Young's char- acterizations are valid on this class as well. In Chapter 7 we discussed shortest path games and have shown that this game class is equal to the class of monotone games. We have shown that further axiomatizations of the Shapley value, namely Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s characterizations are valid on the class of shortest path games

Core and Bargaining Set of Shortest Path Games

In this paper it is shown that the core and the bargaining sets of Davis-Maschler and Zhou coincide in a class of shortest path games.Shortest path games; core; bargaining set

Dominating Set Games

In this paper we study cooperative cost games arising from domination problems on graphs.We introduce three games to model the cost allocation problem and we derive a necessary and su cient condition for the balancedness of all three games.Furthermore we study concavity of these games.game theory;cost allocation;cooperative games