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Motivated by the prevalence of ride-sharing platforms, in “Spatial Pricing in Ride-Sharing Networks,” Bimpikis, Candogan, and Saban explore the impact of the demand pattern for rides across a network’s locations on a platform’s optimal pricing and compensation policy, profits, and consumer surplus. They explicitly account for the pricing problem’s spatial dimension and the fact that the drivers endogenously determine whether and where to provide service. Their first contribution is to develop a tractable model to study a platform operating on a network of locations that may differ in both the size of their potential demand and the destination preferences of riders. Second, they provide a characterization of the platform’s optimal policy and identify “balancedness” of the demand pattern as a property that captures the profit potential of a given network. Finally, they discuss the benefits and limitations of a number of alternative pricing and compensation schemes.

The random priority (RP) mechanism is a popular way to allocate n objects to n agents with strict ordinal preferences over the objects. In the RP mechanism, an ordering over the agents is selected uniformly at random; the first agent is then allocated his most-preferred object, the second agent is allocated his most-preferred object among the remaining ones, and so on. The outcome of the mechanism is a bi-stochastic matrix in which entry (i, a) represents the probability that agent i is given object a. It is shown that the problem of computing the RP allocation matrix is #P-complete. Furthermore, it is NP-complete to decide if a given agent i receives a given object a with positive probability under the RP mechanism, whereas it is possible to decide in polynomial time whether or not agent i receives object a with probability 1. The implications of these results for approximating the RP allocation matrix as well as on finding constrained Pareto optimal matchings are discussed.

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This article describes the optimization process used to schedule the First Division of Argentina's professional volleyball league. The teams in the league are grouped into couples and matches are held on Thursdays and Saturdays. In every pair of consecutive Thursday-Saturday matches, the two teams in each couple play against two teams from another couple. Minimization of travel distances is critical since the teams' home locations are scattered throughout the country and teams do not return their home sites between consecutive away matches, making this problem a variation of the well-known traveling tournament problem. The coupled format gives rise to two key decisions: (a) how to couple the teams and (b) how to schedule the matches. We apply integer programming techniques and a tabu search heuristic to solve these issues. The resulting schedules have been successfully used in

Problem definition: We consider a platform that charges commission rates and subscription fees to sellers and buyers for facilitating transactions but does not directly control the transaction prices, which are endogenously determined. Buyers and sellers are divided into types, and we represent the compatibility between different types using a bipartite network. Traders are heterogeneous in terms of their valuations, and different types have possibly different value distributions. Buyers may have additional value for trading with some seller types. The platform chooses commissions/subscriptions to maximize its revenues. Academic/practical relevance: Two salient features of most online platforms are that they do not dictate the transaction prices, and they use commissions/subscriptions for extracting revenues. We shed light on how these commissions/subscriptions should be set in networked markets. Methodology: Using tools from convex optimization and combinatorial optimization, we obtain tractable methods for computing the optimal commissions/subscriptions and provide insights into the platform’s revenues, buyer/seller surplus, and welfare. Results: We provide a tractable convex optimization formulation to obtain the revenue-maximizing commissions/subscriptions, and establish that, typically, different types should be charged different commissions/subscriptions depending on their network positions. We establish that the latter result holds even when the traders on each side have identical value distributions, and in this setting we provide lower and upper bounds on the platform’s revenues in terms of the supply-demand imbalance across the network. Motivated by simpler schemes used in practice, we show that the revenue loss can be unbounded when all traders on the same side are charged the same commissions/subscriptions, and bound the revenue loss in terms of the supply-demand imbalance across the network. Charging only buyers or only sellers leads to at least half of the optimal revenues, when different types on the same side can be charged differently. Managerial implications: Our results highlight the suboptimality of commonly used payment schemes and showcase the importance of accounting for the compatibility between different user types.