Ridesharing platforms match drivers and riders to trips, using dynamic prices to balance supply and demand. A challenge is to set prices that are appropriately smooth in space and time, in the sense that drivers will choose to accept their dispatched trips, rather than drive to another area or wait for higher prices or a better trip. We introduce the Spatio-Temporal Pricing (STP) mechanism. The mechanism is incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to accept their dispatches, and the mechanism is welfare-optimal, envy-free, individually rational and budget balanced from any history onward. We work in a complete information, discrete time, multi-period, multi-location model, and prove the existence of anonymous, origin-destination, competitive equilibrium (CE) prices. The STP mechanism employs driver-pessimal CE prices, and the proof of incentive alignment makes use of the $M^\natural$ concavity of min-cost flow objectives. The same connection to min-cost flow problems provides an efficient algorithm to compute an optimal matching and prices. We also give an impossibility result, that there can be no dominant-strategy mechanism with the same economic properties. An empirical analysis conducted in simulation suggests that the STP mechanism can achieve significantly higher social welfare than a myopic pricing mechanism, and highlights the failure of incentive alignment due to non-smooth prices in myopic mechanisms.
A coordination problem exists when assigning resources or tasks to agents. Consider assigning spaces in a spinning class for example, or time slots for a neighborhood electric vehicle recharging station, or shifts to volunteers in a child care co-op. In each case, the assignment decision is associated with an intended action and the problem is to coordinate about future actions in the presence of uncertainty, self interest and private information. Coordination success or failure depends on follow-through by agents (e.g., attending the spinning class or not, using the charging station or not, showing up for the assigned shift or not). We want to maximize the probability that agents adopt their assigned role (e.g., maximizing the expected number of agents who attend the spinning class, use the charging station, or show up to the co-op at designated times).
In our model, each agent has private information about its value distribution for different assignment. A mechanism elicits information about value distributions, using this information to determine an assignment along with payments, including payments that are contingent on an agent's future action. Once assigned, each agent later realizes its value and decides how to act. We seek dominant strategy, no deficit mechanisms with voluntary participation, that maximize the expected number of agents who adopt the intended action subject to a natural design constraints. For allocating a single resource, we propose a contingent second-price (CSP) mechanism, prove that CSP is unique under a set of desired criteria, and that CSP is optimal across a larger class of mechanisms. We extend the mechanism to assigning multiple, identical resources (the spinning class) and multiple, heterogeneous resources (charging station, co-op shifts), providing theoretical and experimental justification for the performance of generalized CSP mechanisms.
Without monetary payments, the Gibbard-Satterthwaite theorem proves that under mild requirements all truthful social choice mechanisms must be dictatorships. When payments are allowed, the Vickrey-Clarke-Groves (VCG) mechanism implements the value-maximizing choice, and has many other good properties: it is strategy-proof, onto, deterministic, individually rational, and does not make positive transfers to the agents. By Roberts' theorem, with three or more alternatives, the weighted VCG mechanisms are essentially unique for domains with quasi-linear utilities. The goal of this paper is to characterize domains of non-quasi-linear utilities where ``reasonable'' mechanisms (with VCG-like properties) exist. Our main result is a tight characterization of the maximal non quasi-linear utility domain, which we call the largest parallel domain. We extend Roberts' theorem to parallel domains, and use the generalized theorem to prove two impossibility results. First, any reasonable mechanism must be dictatorial when the utility domain is quasi-linear together with any single non-parallel type. Second, for richer utility domains that still differ very slightly from quasi-linearity, every strategy-proof, onto and deterministic mechanism must be a dictatorship.
Power companies such as Southern California Edison (SCE) uses Demand Response (DR) contracts to incentivize consumers to reduce their power consumption during periods when demand forecast exceeds supply. Current mechanisms in use offer contracts to consumers independent of one another, do not take into consideration consumers' heterogeneity in consumption profile or reliability, and fail to achieve high participation. We introduce DR-VCG, a new DR mechanism that offers a flexible set of contracts (which may include the standard SCE contracts) and uses VCG pricing. We prove that DR-VCG elicits truthful bids, incentivizes honest preparation efforts, enables efficient computation of allocation and prices. With simple fixed-penalty contracts, the optimization goal of the mechanism is an upper bound on probability that the reduction target is missed. Extensive simulations show that compared to the current mechanism deployed in by SCE, the DR-VCG mechanism achieves higher participation, increased reliability, and significantly reduced total expenses.
Demand-side response (DR) is emerging as a crucial technology to assure stability of modern power grids. The uncertainty about the cost agents face for reducing consumption imposes challenges in achieving reliable, coordinated response. In recent work, [Ma et al. 2016] introduce DR as a mechanism design problem and solve it for a setting where an agent has a binary preparation decision and where, contingent on preparation, the probability an agent will be able to reduce demand and the cost to do so are fixed. We generalize this model to allow uncertainty in agents' costs of responding, and also multiple levels of effort agents can exert in preparing. For both cases, the design of contingent payments now affects the probability of response. We design a new, truthful and reliable mechanism that uses a “reward-bidding” approach rather than the “penalty-bidding” approach. It has good performance when compared to natural benchmarks. The mechanism also extends to handle multiple units of demand response from each agent.
We study the problem of incentivizing reliable demand-response in modern electricity grids. Each agent is uncertain about her future ability to reduce demand and unreliable. Agents who choose to participate in a demand-response scheme may be paid when they respond and penalized otherwise. The goal is to reliably achieve a demand reduction target while selecting a minimal set of agents from those willing to participate. We design incentive-aligned, direct and indirect mechanisms. The direct mechanism elicits both response probabilities and costs, while the indirect mechanism elicits willingness to accept a penalty in the case of non-response. We benchmark against a spot auction, in which demand reduction is purchased from agents when needed. Both the direct and indirect mechanisms achieve the reliability target in a dominant-strategy equilibrium, select a small number of agents to prepare, and do so at low cost and with much lower variance in payments than the spot auction.
The existence of truthful social choice mechanisms strongly depends on whether monetary transfers are allowed. Without payments there are no truthful, non-dictatorial mechanisms under mild requirements, whereas the VCG mechanism guarantees truthfulness along with welfare maximization when there are payments and utility is quasi-linear in money. In this paper we study mechanisms in which we can use payments but where agents have non quasi-linear utility functions. Our main result extends the Gibbard-Satterthwaite impossibility result by showing that, for two agents, the only truthful mechanism for at least three alternatives under general decreasing utilities remains dictatorial. We then show how to extend the VCG mechanism to work under a more general utility space than quasi-linear (the “parallel domain”) and show that the parallel domain is maximal—no mechanism with the VCG properties exists in any larger domain.