The Competitive Pickup and Delivery Orienteering Problem for Balancing Car-Sharing Systems

Competition between one-way car-sharing operators is currently increasing. Fleet relocation as a means to compensate demand imbalances constitutes a major cost factor in a business with low profit margins. Existing decision support models have so far ignored the aspect of a competitor when the fleet is rebalanced for better availability. We present mixed-integer linear programming formulations for a pickup and delivery orienteering problem under different business models with multiple (competing) operators. Structural solution properties, including existence of equilibria and bounds on losses as a result of competition, of the competitive pickup and delivery problem under the restrictions of unit-demand stations, homogeneous payoffs, and indifferent customers based on results for congestion games are derived. Two algorithms to find a Nash equilibrium for real-life instances are proposed. One can find equilibria in the most general case; the other can only be applied if the game can be represented as a congestion game, that is, under the restrictions of homogeneous payoffs, unit-demand stations, and indifferent customers. In a numerical study, we compare different business models for car-sharing operations, including a merger between operators and outsourcing relocation operations to a common service provider (coopetition). Gross profit improvements achieved by explicitly incorporating competitor decisions are substantial, and the presence of competition decreases gross profits for all operators (compared with a merger). Using a Munich, Germany, case study, we quantify the gross profit gains resulting from considering competition as approximately 35% (over assuming absence of competition) and 12% (over assuming that the competitor is omnipresence) and the losses because of the presence of competition to be approximately 10%.

Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time

In general, the unit-demand envy-free pricing problem has proven to be APX-hard, but some special cases can be optimally solved in polynomial time. When substitution costs that form a metric space are included, the problem can be solved in O(n4) time, and when the number of consumers is equal to the number of items—all with a single copy so that each consumer buys an item—a O(n3) time method is presented to solve it. This work shows that the first case has similarities with the second, and, by exploiting the structural properties of the costs set, it presents a O(n2) time algorithm for solving it when a competitive equilibrium is considered or a O(n3) time algorithm for more general scenarios. The methods are based on a dynamic programming strategy, which simplifies the calculations of the shortest paths in a network; this simplification is usually adopted in the second case. The theoretical results obtained provide efficiency in the search for optimal solutions to specific revenue management problems.

Optimal Monopoly Mechanisms with Demand Uncertainty

This paper analyzes a monopoly firm’s profit-maximizing mechanism in the following context. There is a continuum of consumers with a unit demand for a good. The distribution of the consumers’ valuations is given by one of two possible demand distributions/states. The consumers are uncertain about the demand state, and they update their beliefs after observing their own valuation for the good. The firm is uncertain about the demand state but infers it from the consumers’ reported valuations. The firm’s problem is to maximize profits by choosing an optimal mechanism among the class of anonymous, deterministic, direct revelation mechanisms that satisfy interim incentive compatibility and ex post individual rationality. We show that, under certain sufficient conditions, the firm’s optimal mechanism is to set the monopoly price in each demand state. Under these conditions, Segal’s optimal ex post mechanism is robust to relaxing ex post incentive compatibility to interim incentive compatibility.

Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

We characterize when a stable and strategy-proof mechanism is guaranteed to exist in the setting of many-to-one matching with contracts. We introduce three novel conditions—observable substitutability, observable size monotonicity, and non-manipulability via contractual terms—and show that when these conditions are satisfied, the cumulative offer mechanism is the unique mechanism that is stable and strategy-proof (for workers). Moreover, we show that our three conditions are, in a sense, necessary: If the choice function of some firm fails any of our three conditions, we can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. Thus, our results provide a rationale for the ubiquity of cumulative offer mechanisms in practice.

Preserving Bidder Privacy in Assignment Auctions: Design and Measurement

Motivated by bidders’ interests in concealing their private information in auctions, we propose an ascending clock auction for unit-demand assignment problems that economizes on bidder information revelation, together with a new general-purpose measure of information revelation. Our auction uses an iterative partial reporting design such that for a given set of prices, not all bidders are required to report their demands, and when they are, they reveal a single preferred item at a time instead of all. Our design can better preserve bidder privacy while maintaining several good properties: sincere bidding is an ex post Nash equilibrium, ending prices are path independent, and efficiency is achieved if the auction starts with the auctioneer’s reservation values. Our measurement of information revelation is based on Shannon’s entropy and can be used to compare a wide variety of auction and nonauction mechanisms. We propose a hybrid quasi–Monte Carlo procedure for computing this measure. Our numerical simulations show that our auction consistently outperforms a full-reporting benchmark with up to 18% less entropy reduction and scales to problems of over 100,000 variables. This paper was accepted by Chris Forman, information systems.

Strategy-Proof and Non-Wasteful Multi-Unit Auction via Social Network

Auctions via social network, pioneered by Li et al. (2017), have been attracting considerable attention in the literature of mechanism design for auctions. However, no known mechanism has satisfied strategy-proofness, non-deficit, non-wastefulness, and individual rationality for the multi-unit unit-demand auction, except for some naïve ones. In this paper, we first propose a mechanism that satisfies all the above properties. We then make a comprehensive comparison with two naïve mechanisms, showing that the proposed mechanism dominates them in social surplus, seller's revenue, and incentive of buyers for truth-telling. We also analyze the characteristics of the social surplus and the revenue achieved by the proposed mechanism, including the constant approximability of the worst-case efficiency loss and the complexity of optimizing revenue from the seller's perspective.