In this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited. We introduce two types of cooperative games—fixed-route traveling salesman games and traveling salesman games—as a tool to attack this problem. Under very mild conditions we prove that fixed-route traveling salesman games have non-empty cores if the fixed route is a solution of the classical traveling salesman problem. Core elements provide us with fair cost allocations. A traveling salesman game may have an empty core, even if the cost matrix satisfies the triangle inequality. In this paper we introduce a class of matrices defining TS-games with non-empty cores.

Traveling salesman games

Supplier-initiated outsourcing: A methodology to exploit synergy in transportation

Nonwmmetric Shapley values for coalitional form games with transferable utility are studied. The nonsymmetries are modeled through nonsymmetric weight systems defined on the players of the games. It is shown axiomatically that two families of solutions of this type are possible. These families are strongly related to each other through the duality relationship on games. While the first family lends itself to applications of nonsymmetric revenue sharing problems the second family is suitable for applications of cost allocation problems. The intersection of these two families consists essentially of the symmetric Shapley value. These families are also char- acterized by a prObabilistic arrival time to the game approach. It is also demonstrated that lack of symmetries may arise naturally when players in a game represent nonequal size constituencies.

On Weighted Shapley Values

Because greenhouse-gas (GHG) emissions from the supply chains of just the 2,500 largest global corporations account for more than 20% of global emissions, rationalizing emissions in supply chains c...

Incentives and Emission Responsibility Allocation in Supply Chains

Sharing costs in highways: A game theoretic approach

Family sequencing and cooperation

Highway games on weakly cyclic graphs

Game theoretic analysis of sequencing situations has been restricted to manufacturing systems which consist of machines that can process only one job at a time. However, in many manufacturing systems, operations are carried out by batch machines which can simultaneously process multiple jobs. This paper aims to extend the game theoretical approach to the cost allocation problems arising from sequencing situations on systems that consist of batch machines. To analyze the allocation problem at hand, it focusses on the existence of core elements, convexity, and the Shapley value.

/pdf/batch-sequencing-and-cooperation-2lpmw08huc.pdf

Batch sequencing and cooperation

A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.

/pdf/population-monotonic-path-schemes-for-simple-games-3tn6tstif6.pdf

Population monotonic path schemes for simple games

In this paper, we consider spanning tree situations, where players want to be connected to a source as cheap as possible. These situations involve the construction of a spanning tree with the minimum cost as well as the allocation of the cost of this minimum cost spanning tree among its users in a fair way. Feltkamp, Muto and Tijs 1994 introduced the equal remaining obligations rule to solve the cost allocation problem in these situations. Recently, it has been shown that the equal remaining obligations rule satisfies many appealing properties and can be obtained with different approaches. In this paper, we provide a new approach to obtain the equal remaining obligations rule. Specifically, we show that the equal remaining obligations rule can be obtained as the average of the cost allocations provided by a vertex oriented construct-and-charge procedure for each order of players.

Barış Çiftçi

Papers

Family sequencing and cooperation

Highway games on weakly cyclic graphs

Batch sequencing and cooperation

Population monotonic path schemes for simple games

A vertex oriented approach to the equal remaining obligations rule for minimum cost spanning tree situations