arXiv:2201.00061v1 [math.OC] 31 Dec 2021 The value of shared information in ridesharing problems: a stochastic Stackelberg game approach Gianfranco Liberona * L´ eonard von Niederh¨ ausern † David Salas ‡ Abstract In the setting of stochastic Stackelberg games, we introduce a new indicator called the Ex- pected Value of Shared Information. This indicator allows to measure, for the leader, the value of having perfect information and sharing it with the follower, in the context where both agents must solve here-and-know problem, making their decisions prior to the revelation of nature. We then use it to assess the value of sharing information in the context of ridesharing com- panies. Particularly, we study a simplified version of the reallocation problem of unmatched drivers. Our results suggest that sharing information (such as the demand forecast) with the drivers might be beneficial for the company. Keywords: Game Theory; Stochastic Programming; Ridesharing Company; Stackelberg Game; Expected Value of Shared Information. 1 Introduction The growing popularity of ridesharing companies, such as Uber and Lyft, has changed the way we move around the city. There is a new relation between passengers and drivers, which now interact through this new third party. Several new problems have arisen from this context, such as spatio-temporal pricing [7], reallocation of resources [2, 15], or online matching [16] (see, e.g., [24, 5] for some recent surveys). Here, we are interested in the way information affects the relation between a ridesharing company and its drivers. To understand this relation, let us describe the general framework we are set in, which is motivated by recent literature [24, 5, 7]. First, a city can be understood as a network of inter- connected locations, to which drivers are allocated. At every given time, new passengers appear in the locations, requesting a ride. The ridesharing company then matches each passenger with a driver in the same location, and receives a compensation proportional to the cost of the ride. While the compensation can be assumed to be constant, the company has the liberty to adapt prices, generating different fares depending on the location and time. Of course, pricing affects the demand. But more interesting for us, spatial pricing (different fares between locations) can induce reallocation of unmatched drivers. Some key elements for an unmatched driver to decide whether to change location or not are the following: the available ride fares, the costs of reallocation, the number of demanded * Universidad de O’Higgins. gianfranco.liberona@uoh.cl † Center of Mathematical Modeling CNRS IRL 2807, Universidad de Chile, and Institute of Engineering Sciences, Universidad de O’Higgins. leonard.vonniederhausern@uoh.cl ‡ Institute of Engineering Sciences, Universidad de O’Higgins. david.salas@uoh.cl 1