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Spatio-Temporal Pricing for Ridesharing Platforms

Hongyao Ma, Fei Fang, David C. Parkes

arXiv:1801.04015v5cs.GTcs.MA

TL;DR

Ridesharing pricing can misprice trips and encourage drivers to decline dispatches when spatial and temporal supply-demand conditions vary. The paper introduces the Spatio-Temporal Pricing mechanism (STP), under which drivers always accepting dispatches is a subgame-perfect equilibrium; it also identifies a boundary on rider truthfulness.

  • Problem

    Mispricing trips can incentivize drivers to cherry-pick, while origin-based surge pricing can overlook destination conditions and encourage declines to low-payoff locations.

    Source: §1 · p. 2

  • Method

    The paper proposes a simple ridesharing pricing-and-dispatch framework incorporating spatial imbalance and temporal variation, together with the STP mechanism.

    Source: §1.1 · p. 3

  • Results

    Under STP, drivers always accepting dispatched trips forms a subgame-perfect equilibrium, and the mechanism strictly balances budget.

    Source: §6 · pp. 30–31

  • Takeaways & Limitations

    The framework is presented as the first in the literature rich enough to incorporate spatial imbalance and temporal variation in supply and demand.

    Source: §1.1 · p. 3

    STP is not truthful for riders, and no budget-balanced core-selecting mechanism is truthful for riders.

    Source: §6 · p. 32

Abstract

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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, so that drivers with the flexibility to decide how to work will nevertheless choose to accept their dispatched trips, rather than drive to another area or wait for higher prices or a better trip. In this work, we propose a complete information model that is simple yet rich enough to incorporate spatial imbalance and temporal variations in supply and demand -- conditions that lead to market failures in today's platforms. We introduce the Spatio-Temporal Pricing (STP) mechanism. The mechanism is incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to always accept their trip dispatches. From any history onward, the equilibrium outcome of the STP mechanism is welfare-optimal, envy-free, individually rational, budget balanced, and core-selecting. We also prove the impossibility of achieving the same economic properties in a dominant-strategy equilibrium. Simulation results show that the STP mechanism can achieve substantially improved social welfare and earning equity than a myopic mechanism.

1 Introduction

Ridesharing platforms’ spatial and temporal mispricing can prompt drivers to reject trips, relocate, or wait offline, undermining reliable service and driver flexibility. The paper introduces a multi-location, multi-period model and STP, then establishes incentive and welfare properties and reports simulation gains over myopic pricing.

1 Introduction

  • Spatial and temporal mispricing, including origin-based prices that ignore destinations, encourages drivers to chase surge, wait offline, or reject trips with low continuation payoffs.These behaviors can make reliable access difficult for riders and contribute to earnings inequity.Source: §1 · pp. 2–3

1.1 Our results

  • The model combines complete information and multiple locations and periods with variation in trips, rider values, and driver availability, entry, and exit.It assumes riders are impatient and price-taking and drivers have common costs for the same trip, without idiosyncratic preferences over riders or locations.Source: §1.1 · p. 4
  • STP uses driver-pessimal competitive-equilibrium plans and updates downstream plans after deviations, making acceptance of dispatched trips a subgame-perfect equilibrium.The paper reports welfare-optimality, incentive alignment, envy-freeness, and core selection among the mechanism’s properties.Source: §1.1 · pp. 3–5
  • STP’s equilibrium outcomes are welfare-optimal, envy-free, and core-selecting, while the paper proves these economic properties cannot all be achieved in a dominant-strategy mechanism.The listed properties also include welfare-optimality and incentive alignment.Source: §1.1 · pp. 3, 5
  • Simulations across three stylized scenarios report substantially higher social welfare under STP than myopic pricing, which also exhibits incentive-alignment failures and high variance in driver earnings.The scenarios cover an event ending, morning rush hour, and unbalanced airport flows.Source: §1.1 · p. 5

1.2 Related Work

  • Unlike stationary or continuum pricing models discussed in the related work, this framework considers multiple locations and periods with supply and demand varying across both.The paper describes this joint spatial-temporal scope as unique to its work.Source: §1.2 · p. 5

2 Preliminaries

The preliminaries model drivers’ and riders’ choices over a finite time-and-location horizon, then use a Super Bowl example to show how myopic origin-based pricing can fail.

2 Preliminaries

  • The model represents trips across discrete locations and times, with travel durations, driver costs, entry and exit choices, and riders’ requested trips and values.It assumes complete, symmetric information about supply, demand, and participant types over the planning horizon.Source: §2 · pp. 7–8
  • The myopic baseline allocates available drivers by nonnegative per-period rider surplus at each origin and sets origin-based prices without accounting for future supply and demand.Its simplicity comes with failures to optimize welfare or provide spatially and temporally smooth prices.Source: §2 · p. 10
  • Welfare is only 25 under myopic pricing in the Super Bowl example, and the mechanism can achieve no constant fraction of optimal welfare.The example’s myopic dispatches and exit choices produce the welfare of 25.Source: §2 · p. 10
  • At the Super Bowl, myopic prices jump from 10 to at least 100 for C-to-B trips in one period, while neighboring-location prices can differ sharply.The price for B-to-B at time 1 is 10, compared with at least 100 for C-to-B.Source: §2 · p. 11
  • Myopic origin-based prices can reward strategic deviation: a driver who waits in C can earn at least 25 utility, versus at most 5 by following dispatches.The example also reports unequal payoffs for drivers starting at the same location and time.Source: §2 · p. 11

3 A Static CE Mechanism

The section establishes competitive-equilibrium plans’ welfare and fairness guarantees, then shows that freezing or repeatedly recomputing plans creates distinct strategic weaknesses.

3.1 Plans

  • Plans specify rider pickups, driver action paths, and payments; anonymous trip prices charge riders and pay dispatched drivers the same amount for a given trip, ensuring strict budget balance.Source: §3.1 · pp. 11–12

3.2 Optimal Plans and CE Prices

  • The welfare-planning linear program has an integer optimum, enabling efficient computation through its reduction to minimum-cost flow.The reduction uses a network whose vertices are location-time pairs and whose edges represent trips.Source: §3.2 · p. 13
  • A welfare-optimal dispatch exists as a competitive-equilibrium plan, and every such plan is strictly budget-balanced, individually rational, and envy-free for riders and drivers.The welfare theorem also states that welfare-optimality is equivalent to the existence of supporting anonymous trip prices.Source: §3.2 · p. 14
  • Driver utilities across CE outcomes form a lattice; each driver’s utility in the driver-pessimal or driver-optimal plan equals the corresponding welfare gain or loss.These extremal utilities connect the CE price choices to the welfare effects of adding or losing a driver.Source: §3.2 · p. 14
  • All CE plans are in the core, and every budget-balanced core outcome has an anonymous-price CE representation with the same participant utilities.Source: §3.2 · p. 15
  • In the Super Bowl example, the driver-pessimal CE plan yields welfare 215 versus 25 under myopic pricing, with prices rising more smoothly ahead of future demand.The CE plan keeps or repositions drivers at C to serve high-value riders; sending a driver away before the game ends is reflected in higher earlier prices.Source: §3.2 · p. 15

3.3 The Static CE Mechanism

  • A static CE mechanism announces one CE plan and makes following its dispatch a dominant strategy; when all follow, its outcome is budget-balanced and envy-free.The static plan does not update after deviations, making later outcomes potentially unreliable or welfare-suboptimal.Source: §3.3 · p. 16
  • Repeatedly recomputing driver-pessimal plans can fail incentive compatibility, and truthful rider-value reporting need not be dominant under any CE-price selection.The section frames robustness and the strategic effects of deviation-triggered replanning as the challenge.Source: §3.3 · pp. 16–17

4 The Spatial-Temporal Pricing Mechanism

This section defines the STP mechanism and examines incentive compatibility under its dispatches, including how its driver-pessimal CE payments prevent an illustrated profitable deviation. It also states the welfare and fairness properties of its equilibrium outcome and contrasts STP with driver-optimal CE pricing and dynamic VCG, which can leave drivers incentives to reject dispatches.

4.1 A Dynamic Mechanism

  • A dynamic ridesharing mechanism uses history-dependent dispatch and payment rules, while temporal consistency requires its post-deviation plan to match a fresh plan for the resulting state.Drivers choose whether to follow dispatches or take available alternatives.Source: §4.1 · pp. 17, 18, 20

4.2 The Spatio-Temporal Pricing Mechanism

  • STP plans or replans after deviations by optimizing an LP for dispatches and setting anonymous trip prices for driver and rider payments.It dispatches all available drivers, and can recompute the plan from the economy following a deviation.Source: §4.2 · p. 21
  • STP is temporally consistent and subgame-perfect incentive compatible; its equilibrium outcome from any history onward is welfare-optimal, core-selecting, envy-free, and individually rational for drivers.It is individually rational for riders and strictly budget balanced under any driver action profile.Source: §4.2 · p. 21
  • No dynamic ridesharing mechanism can make following dispatches a dominant strategy while guaranteeing history-wise welfare optimality, rider individual rationality, budget balance, and envy-freeness for riders and drivers.The impossibility applies when all four properties are required from any history onward.Source: §4.2 · p. 22
  • Under driver-optimal CE pricing, a driver can reject a dispatch, trigger plan recomputation, and obtain a higher continuation payment as her marginal product rises over time.In the example, the updated price for rider 2’s trip is 5, higher than driver 1’s payment for following the dispatches.Source: §4.2 · p. 23
  • STP avoids this useful deviation because driver-pessimal CE payments reflect the additional welfare from replicating a driver, which is non-increasing over time.It is always more useful to have an extra driver earlier.Source: §4.2 · p. 24
  • Dynamic VCG, equivalent to shifting driver-optimal payments over time, also fails to align incentives because drivers may face negative payments and decline dispatches to avoid them.The passage argues that the challenge is incentive alignment without time-extended contracts, rather than information asymmetry.Source: §4.2 · p. 24

5 Simulation Results

The simulations compare STP with myopic pricing in three stylized settings. Overall, STP achieves substantially higher social welfare and driver time-efficiency, while myopic pricing produces unstable prices and high driver regret.

5 Simulation Results

  • Across three stylized scenarios, STP achieves substantially higher social welfare and driver time-efficiency than myopic pricing, whose prices are unstable and driver regret high.The comparison uses 1,000 randomly generated economies in each scenario.Source: §5 · p. 24

5.1 Scenario One: The End of a Sporting Event

  • As event-end C→B demand rises, STP sends more drivers to C, maintains smoother prices and zero regret, and raises welfare, though its driver time-efficiency falls.Myopic pricing sends all drivers starting at C to B, leaving an average of only five drivers to travel from B to C at time 1.Source: Figure 9 · p. 25, §5.1 · pp. 25–26, Figure 12 · p. 26

5.2 Scenario Two: The Morning Rush Hour

  • In the morning rush-hour scenario, STP achieves higher welfare and driver time-efficiency, repositioning drivers toward C while myopic pricing sends drivers along poorly matched routes.STP also prices the B→C trip near zero to encourage movement toward future commuter demand at C.Source: §5.2 · pp. 27–28, Figure 18 · p. 29

5.3 Scenario Three: Unbalanced Airport Trips

  • With more balanced airport trip flows, STP welfare and driver time-efficiency rise; as flows skew, myopic performance drops quickly while STP driver counts remain stable.Airport-direction price surges are lower under STP than under myopic pricing.Source: §5.3 · pp. 29–30, Figure 19 · p. 30, Figure 20 · p. 30

6 Concluding Remarks

The concluding remarks describe STP as a way to align driver incentives while preserving welfare-oriented pricing, and identify assumptions and extensions that bound the paper’s scope. The appendices outline the model interpretation and supporting optimization proofs.

6 Concluding Remarks

  • STP computes a driver-pessimal competitive-equilibrium plan initially and after deviations, using marginal welfare contributions at trip origins and destinations to guide smooth prices.The authors identify this pricing insight as central to optimizing social welfare.Source: §6 · p. 31
  • Welfare, rather than platform revenue, is the objective; the authors connect that choice to growth priorities and public or nonprofit platform operation.STP strictly balances its budget; taking a fixed fraction of driver surplus leaves results intact but places outcomes in an ε-core dependent on the fraction.Source: §6 · p. 31
  • The analysis assumes homogeneous driver costs, drivers staying through the horizon, and impatient riders; relaxing either of the latter assumptions may break LP integrality and anonymous origin-destination CE price existence.Shorter periods also make full rider impatience less likely and weaken envy-freeness.Source: §6 · p. 31
  • The model assumes complete information and a finite horizon; the authors identify uncertain supply and demand with a rolling horizon as a natural extension.They note that continuation values may lose M♮-concavity, potentially affecting integrality and competitive-equilibrium existence.Source: §6 · p. 31
  • The paper focuses on dynamic incentive alignment while maintaining driver flexibility, rather than on information asymmetry.The conclusion notes that driver entrance information could instead be elicited, but the supplied passage does not detail those results.Source: §6 · p. 31

Appendix

  • The appendices collect omitted proofs, examples on integrality and competitive-equilibrium existence, incentive discussions, related-work analysis, and additional simulations..Source: Appendix · p. 36

A Continuous Time Interpretation

  • The continuous-time interpretation treats within-location travel and between-location travel as taking one and two periods, respectively.The example permits drop-off and pickup at the same discrete time point, with within-location travel occurring between them.Source: Figure 21 · p. 36, A Continuous Time Interpretation · p. 36

B Proofs

  • The proof appendix establishes that a competitive-equilibrium plan remains a CE after converting to anonymous prices, with the same driver and rider payments and utilities.The optimal-dispatch problem is reduced to minimum-cost flow on location-time nodes, with rider-trip edges carrying trip costs minus rider values.Source: §B.1 · pp. 36–37, §B.2.1 · p. 37, §B.2.2 · p. 37

B.2.3 Proof of Lemma 2

This proof establishes integrality of the optimal-dispatch LP by relating it to a minimum-cost flow formulation.

B.2.3 Proof of Lemma 2

  • The optimal-dispatch LP has an integer optimal solution because it corresponds to an integral minimum-cost flow LP with the same objective.Feasible solutions map between the formulations, and integral flow solutions decompose into driver paths.Source: §B.2.3 · pp. 39–40
  • The flow formulation uses a polynomial number of variables and constraints in |R|, |L|, and T, unlike the original LP’s exponentially many feasible-path variables.The reduction also allows the original problem to be solved efficiently using network-flow algorithms.Source: §B.2.3 · p. 40

B.3 Proof of Lemma 3

The proof connects welfare-optimal dispatches to competitive equilibria with anonymous trip prices, then uses dual-flow correspondences to establish existence and economic properties.

B.3 Proof of Lemma 3

  • In a CE, a trip taken by a driver has a non-positive anonymous price when a driver also uses it for relocation without a rider.The proof explains that a positive price would make the driver better off by being paid for that relocation trip.Source: §B.3 · p. 40
  • A dispatch is welfare-optimal exactly when anonymous trip prices make it a competitive equilibrium; such plans exist, are efficiently computable, strictly budget balanced, individually rational, and envy-free for riders and drivers.The proof obtains the correspondence through primal-dual optimality and complementary slackness.Source: §B.3 · p. 41

B.4.1 Dual of the Flow LP

  • The optimal solutions of the original dual and the flow-LP dual correspond one-to-one on driver and rider utilities.The flow-dual variables represent drivers’ continuation payoffs and riders’ utilities.Source: §B.4.1 · p. 43

B.4.2 Proof of Lemma 4

The proof establishes a lattice structure for driver utilities across competitive-equilibrium outcomes.

B.4.2 Proof of Lemma 4

  • Drivers’ utility profiles across CE outcomes form a lattice, with ΦDi and ΨDi giving each driver’s utility in the driver-pessimal and driver-optimal CE plans.The proof reduces the claim to the lattice structure of optimal potentials in the flow-LP dual.Source: §B.4.2 · p. 45

Step 1. Proof of the Lattice Structure

The proof establishes a lattice of optimal potentials for the flow problem, then identifies its extremes with welfare changes from adding or losing drivers. The resulting welfare gains correspond to competitive-equilibrium driver utilities.

Step 1. Proof of the Lattice Structure

B.5 Proof of Lemma 5

The proof establishes an equivalence between competitive-equilibrium plans and budget-balanced core outcomes: every CE plan is in the core, and every budget-balanced core outcome has a utility-equivalent CE representation. The representation uses anonymous trip prices but need not preserve each driver’s payment timing.

B.5 Proof of Lemma 5

  • Every competitive-equilibrium plan is in the core, and every budget-balanced core outcome can be represented by an anonymous-price CE with the same total utilities.The constructed CE preserves driver and rider total utilities, not necessarily each driver’s payment at each time.Source: §B.5 · pp. 50–52
  • The proof derives welfare optimality, individual rationality, and strict budget balance as necessary properties of a core outcome.It also establishes equal payments among riders requesting the same trip when picked up.Source: §B.5 · p. 51
  • Anonymous trip prices can preserve a core outcome’s total driver utilities without preserving its time-specific payments.In the example, the core outcome pays one driver 2 then 6, while anonymous prices require payments of 4 in each period.Source: §B.5 · p. 52

B.6 Proof of Theorem 2

Theorem 2 establishes that STP is temporally consistent and subgame-perfect incentive compatible, with welfare-optimal, core-selecting, envy-free, and individually rational equilibrium outcomes from any history. The proof relates driver continuation utilities to welfare gains and rules out profitable single deviations; the appendix also includes further examples and discussions.

B.6 Proof of Theorem 2

  • From any history, STP’s equilibrium outcome is welfare-optimal, core-selecting, envy-free, and individually rational for drivers; the mechanism is subgame-perfect incentive compatible.It is also individually rational for riders and strictly budget balanced for any driver action profile.Source: §B.6 · p. 52
  • Under the STP dispatch, each driver’s total utility equals the welfare gain from replicating that driver, so the resulting plan forms a competitive equilibrium.The proof uses this utility correspondence to establish the CE property at each replanning point.Source: §B.6 · pp. 52–53
  • A driver’s relocation deviation is bounded by the destination’s continuation welfare gain minus travel cost, and the proof shows it is no better than following the dispatch.The argument uses stronger substitution between drivers at the same location and time than between drivers at different locations.Source: §B.6 · pp. 54–56

C Additional Discussions and Examples

C.1 LP Integrality and Existence of CE

Violating either the common-exit-time or related assumptions can destroy LP integrality and the existence of welfare-optimal competitive-equilibrium outcomes. Examples show this for drivers with different exit times and for patient riders.

C.1 LP Integrality and Existence of CE

  • When drivers have different exit times or riders may wait, the LP relaxation can be nonintegral and welfare-optimal competitive-equilibrium outcomes may not exist.Different driver exit times also create heterogeneous flows; preference over final locations can likewise break integrality unless drivers start at the same time and location.Source: §C.1 · pp. 56, 58
  • In Example 6, the fractional LP solution yields social welfare 18.5 (riders 2, 5, and 6 picked up with probability 1 and rider 1 with probability 0.5), exceeding the integral optimum of 18.The price-support failure concerns the optimal integral dispatch: the price bounds create a contradiction in drivers’ incentives.Source: §C.1 · p. 57
  • Different driver exit times break the homogeneous-flow reduction because a flow decomposition can assign a driver to an exit time that is not hers.The example's homogeneous flow has welfare 21 but cannot be implemented with the drivers' actual exit times.Source: §C.1 · p. 57
  • 9.5 LP welfare exceeds the integral optimum of 9 in the patient-rider example, and the optimal integral dispatch is not supported by anonymous origin-destination prices.The patient rider's possible pickup at multiple times creates multiple edges for one rider, making the single-pickup constraint difficult to represent without losing flow integrality.Source: §C.1 · p. 58

C.2 Rider Incentives

The section examines rider-side incentive compatibility and the relation between rider-side VCG payments and competitive-equilibrium prices. It shows that welfare-optimal CE outcomes need not be rider-truthful, while minimum CE trip prices equal rider-side VCG prices for riders picked up in some welfare-optimal dispatch.

C.2 Rider Incentives

  • No welfare-optimal competitive-equilibrium outcome, including STP, makes riders truthfully reporting their values incentive-compatible.In Example 9, a rider charged above her VCG price can profit by reporting that lower value.Source: §C.2 · p. 59
  • Competitive-equilibrium trip prices and rider utilities need not form a lattice, because separately minimizing two trip prices can violate driver best response.In Example 8, the lowest prices for two trips cannot be set together: the resulting price for the other trip would need to be at least 8.Source: §C.2 · p. 59
  • Rider-side VCG prices can fail to support a welfare-optimal CE and can leave a driver with a profitable deviation.In Example 9, the rider-side payments are 2 and 3, while relocating allows the driver to receive a payment of 8 under the updated plan.Source: §C.2 · pp. 59, 61
  • For a rider picked up in some welfare-optimal dispatch, her rider-side VCG price equals the minimum price for her trip across all competitive-equilibrium outcomes.The proof establishes that every CE price is at least the VCG payment and that some CE outcome attains a price no greater than it.Source: §C.2 · pp. 59–61

C.3 Truthful Reporting of Driver Entrance

The section studies truthful reporting of drivers' entrance location and time when that information is private. Truthful reporting is supported under a constrained entry condition, but a replanning example shows that allowing arbitrary later entry can make misreporting profitable.

C.3 Truthful Reporting of Driver Entrance

  • A driver cannot gain by reporting a later entrance location and time if she actually enters there and the reported time is at least her travel time from her true starting point.The theorem assumes the driver follows the subgame-perfect equilibrium after entering; the truthful-payment argument uses the welfare gain from replicating that driver.Source: §C.3 · pp. 61–62
  • The truthful-report result is limited to cases where the driver actually enters at the location and time she reported.With replanning after a reported entrance fails to occur, truthful reporting is not guaranteed when drivers may enter arbitrarily.Source: §C.3 · p. 62
  • Reporting entry at (B, 1) and actually entering at (B, 2) raises the driver's payment from 0 to 4 under replanning, making the misreport profitable.The earlier report changes the first plan; after the driver misses that entry and later enters, the new welfare gain from an additional driver at (B, 2) is 4.Source: §C.3 · p. 63

C.4 Naive Update of Static Plans

Repeatedly updating static driver-optimal CE plans can undermine envy-freeness and, depending on tie-breaking, driver incentives. The section also clarifies that STP does not require bounded price gaps or triangle inequalities for its incentive results.

C.4 Naive Update of Static Plans

  • The mechanism’s repeated recomputation of driver-optimal CE plans can yield a realized outcome that is not envy-free, and may fail incentive compatibility depending on tie-breaking among driver-optimal plans.At time 2, the price for trip (B, B, 2) becomes 10, higher than driver 2’s original payment. Staying at B at time 0 can be useful if driver 2 is assigned path ((B, B, 1), (B, B, 2)) with non-zero probability, as under uniform random tie-breaking.Source: §C.4 · pp. 63–64

C.5 On the Smoothness of Prices

  • STP does not require bounded price gaps: the examples show arbitrarily large spatial or temporal gaps can be necessary or occur in welfare-optimal outcomes.The text also notes that competitive-equilibrium prices are more smooth than myopic prices, while bounded gaps are neither necessary nor sufficient for smoothness in this model.Source: §C.5 · p. 64

C.6 Asymmetry and Triangle Inequality

  • The incentive results do not require triangle inequalities for distances or trip costs, and distances may vary over time without affecting the paper's results.Triangle inequalities do rule out a rider's strategy of splitting a long trip into shorter trips to obtain a lower total price.Source: §C.6 · pp. 64–65

D.1 Dynamic VCG

The appendix explains why dynamic VCG can fail incentive compatibility in ridesharing and why a trading-network formulation does not establish the STP mechanism’s incentive compatibility. It also introduces additional simulation results omitted from the paper’s main body.

D.1 Dynamic VCG

  • With known states and no driver private information, a time-shifted driver-optimal mechanism is equivalent to dynamic VCG in the ridesharing setting.The adaptation assumes homogeneous driver costs and no location preferences.Source: §D.1 · p. 65
  • Driver 1’s dynamic VCG payments total 1 under dispatch, but rejecting at time 0 avoids a negative payment and remains a useful deviation, so the mechanism is not incentive compatible.The example gives payments of −5, 1, and 5 across periods under dispatch; after rejecting, the later payments are 0 and 5.Source: §D.1 · p. 65

D.2 Trading Networks

  • With zero trip and early-exit costs, dispatch can be mapped to a trading network of drivers, riders, and rights to use cars, but this mapping does not establish incentive compatibility for drivers making repeated decisions.In the network formulation, drivers trade the right to use a car over the remaining planning horizon; in the ridesharing setting, they make decisions over time.Source: §D.2 · p. 66

E Additional Simulation Results

  • The appendix presents additional simulation results that were omitted from the paper’s main body.The supplied passage does not describe those results.Source: E Additional Simulation Results · p. 66

E.1 Morning Rush Hour

The morning-rush-hour simulations compare driver counts and prices across five trips not analyzed in Section 5.2. STP sends many drivers from A to C in response to high demand there, while the myopic mechanism leaves drivers around B and does not shift more drivers from A to C than from A to A.

E.1 Morning Rush Hour

  • The additional morning-rush-hour results cover five trips that were not analyzed in Section 5.2.Source: §E.1 · p. 66
  • STP dispatches many drivers from A to C because demand at C is high, while myopic pricing leaves drivers around B and does not shift more drivers from A to C than from A to A.Figure 29 compares the number of drivers per trip in this morning-rush-hour scenario.Source: §E.1 · pp. 66–67, Figure 29 · p. 67
  • The reported trip prices are described as intuitive and easy to interpret.Figure 30 presents the additional morning-rush-hour trip-price comparison.Source: Figure 30 · p. 67, §E.1 · p. 67
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