No abstract

The traveling salesman game (TSG) consists of dividing the cost of a round trip among several customers. One of the most significant solution concepts in cooperative game theory is the Shapley value, which provides a fair division of the costs for a variety of games including the TSG, based on the marginal costs attributed with each customer. In this paper, we consider efficient methods for computing the Shapley value for the TSG. There exist two major variants of the TSG. In the first variant, there exists a fixed order in which the customers are serviced. We show a method for efficient computation of the Shapley value in this setting. Our result is also applicable for efficient computation of the Shapley value in ride-sharing settings, when a number of passengers would like to fairly split their ride cost. In the second variant, there is no predetermined fixed order. We show that the Shapley value cannot be efficiently computed in this setting. However, extensive simulations reveal that our approach for the first variant can serve as an excellent proxy for the second variant, outperforming the state-of-the-art methods.INDEX TERMS Shapley value, Traveling salesman games, Vehicle routing problem.

Ride-sharing services are gaining popularity and are crucial for a sustainable environment. A special case in which such services are most applicable, is the last mile variant. In this variant it is assumed that all the passengers are positioned at the same origin location (e.g. an airport), and each have a different destination. One of the major issues in a shared ride is fairly splitting of the ride cost among the passengers. In this paper we use the Shapley value, which is one of the most significant solution concepts in cooperative game theory, for fairly splitting the cost of a shared ride. We consider two scenarios. In the first scenario there exists a fixed priority order in which the passengers are dropped-off (e.g. elderly, injured etc.), and we show a method for efficient computation of the Shapley value in this setting. Our results are also applicable for efficient computation of the Shapley value in routing games. In the second scenario there is no predetermined priority order. We show that the Shapley value cannot be efficiently computed in this setting. However, extensive simulations reveal that our approach for the first scenario can serve as an excellent proxy for the second scenario, outperforming other known proxies.

We analyze the assignment of passengers in a shared ride, which considers the social relationship among the passengers. Namely, there is a fixed number of passengers in each vehicle, and the goal is to recommend an assignment of the passengers such that the number of friendship relations is maximized. We show that the problem is computationally hard, and we provide an approximation algorithm.