On the Core of Multiple Longest Traveling Salesman Games

In this paper we introduce multiple longest traveling salesman (MLTS) games. An MLTS game arises from a network in which a salesman has to visit each node (player) precisely once, except its home location, in an order that maximizes the total reward.First it is shown that the value of a coalition of an MLTS game is determined by taking the maximum of suitable combinations of one and two person coalitions.Secondly it is shown that MLTS games with ¯ve or less players have a nonempty core.However, a six player MLTS game may have an empty core.For the special instance where the reward between a pair of nodes is equal to 0 or 1, we provide relations between the structure of the core and the underlying network.game theory;traveling salesman problem;games;core

Characterizing the Shapley Value in Fixed-Route Traveling Salesman Problems with Appointments

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to ?nd a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We intro- duce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We characterize the Shapley Value in this class using a property which requires that sponsors do not bene?t from mergers, or splitting into a set of sponsors.Fixed-route travelling salesman games, routing games, appointment games, the Shapley value, the core, transferable-utility games, merging and splitting proofness, networks, cost allocation

On some approximately balanced combinatorial cooperative games

A model of taxation for cooperativen-person games is introduced where proper coalitions Are taxed proportionally to their value. Games with non-empty core under taxation at rateɛ-balanced. Sharp bounds onɛ in matching games (not necessarily bipartite) graphs are estabLished. Upper and lower bounds on the smallestɛ in bin packing games are derived and euclidean random TSP games are seen to be, with high probability,ɛ-balanced forɛ≈0.06

Appointment Games in Fixed-Route Traveling Salesman Problems and the Shapley Value

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to find a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We introduce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We study the Shapley Value in this class and show that it is in the core. Our first characterization of the Shapley value involves a property which requires that sponsors do not benefit from mergers, or splitting into a set of sponsors. Our second theorem involves a property which requires that the cost shares of two sponsors who get connected are equally effected. We also show that except for our second theorem, none of our results for appointment games extend to the class of routing games (Potters et al, 1992).fixed-route traveling salesman games, routing games, appointment games, the Shapley value, the core, transferable-utility games, merging and splitting proofness, equal impact, networks, cost allocation.

Operations Research Games: A Survey

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved.Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players.This interplay between optimisation and allocation is the main subject of the area of operations research games.It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.cooperative games;operational research

On the Core of Routing Games with Revenues

Traveling salesman problems with revenues form a generalization of traveling salesman problems.Here, next to travel costs an explicit revenue is generated by visiting a city.We analyze routing problems with revenues, where a predetermined route on all cities determines the tours along subgroups.Corresponding routing games with revenues are analyzed.It is shown that these games have a nonempty core and a complete description of the core is provided.

On the Core of Multiple Longest Traveling Salesman Games

In this paper we introduce multiple longest traveling salesman (MLTS) games. An MLTS game arises from a network in which a salesman has to visit each node (player) precisely once, except its home location, in an order that maximizes the total reward.First it is shown that the value of a coalition of an MLTS game is determined by taking the maximum of suitable combinations of one and two person coalitions.Secondly it is shown that MLTS games with ¯ve or less players have a nonempty core.However, a six player MLTS game may have an empty core.For the special instance where the reward between a pair of nodes is equal to 0 or 1, we provide relations between the structure of the core and the underlying network.