Theoretical results Ignoring demand dynamics, nave old pricing model - - PowerPoint PPT Presentation

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Theoretical results Ignoring demand dynamics, nave old pricing model - - PowerPoint PPT Presentation

Oct 19, 2022 22 likes β€’62 views

Driver Surge Pricing | Nikhil Garg and Hamid Nazerzadeh We present the theoretical foundation for additive surge, Ubers new driver surge mechanism Theoretically study driver incentives with dynamic pricing Multiplicative surge Show

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Driver Surge Pricing | Nikhil Garg and Hamid Nazerzadeh

We present the theoretical foundation for additive surge, Uber’s new driver surge mechanism

Additive surge Multiplicative surge

Key effect: lock in surge payments with long trips Theoretically study driver incentives with dynamic pricing

  • Show multiplicative surge doesn’t work
  • Develop a pricing scheme that does work

Empirically show that additive surge works in practical regimes of interest

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Theoretical results

Theorem: In the static model, Proportional pricing π‘₯ 𝜐 = π‘›πœ is incentive compatible.

Ignoring demand dynamics, naΓ―ve old pricing model works well. With demand dynamics, it doesn’t.

Theorem: Proportional pricing may not be incentive compatible If payout during surge is proportional, π‘₯1(𝜐) = 𝑛1𝜐 then 𝜏1 = π‘ˆ

1, ∞ , i.e., rejecting short trips, is optimal

With demand dynamics, additive surge approximately works.

Theorem: For

𝑄0 𝑄1 ∈ [𝐷, 1], we have IC prices of the form:

π‘₯𝑗 𝜐 = π‘›π‘—πœ + 𝑨𝑗

πœ‡π‘—β†’π‘˜ πœ‡π‘—β†’π‘˜+πœ‡π‘˜β†’π‘—

1 βˆ’ π‘“βˆ’ πœ‡π‘—β†’π‘˜+πœ‡π‘˜β†’π‘— 𝜐

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Theorem: For

𝑄0 𝑄1 ∈ [𝐷, 1], we have IC prices of the form:

π‘₯𝑗 𝜐 = π‘›π‘—πœ + 𝑨𝑗

πœ‡π‘—β†’π‘˜ πœ‡π‘—β†’π‘˜+πœ‡π‘˜β†’π‘—

1 βˆ’ π‘“βˆ’ πœ‡π‘—β†’π‘˜+πœ‡π‘˜β†’π‘— 𝜐 with 𝑛0, 𝑛1, 𝑨1 β‰₯ 0.

Probability that a trip of length 𝜐 that starts in state 𝑗 ends in state π‘˜ Continuation value: compensate drivers for taking them out of surge We have 𝑛𝑗, 𝑨𝑗, 𝐷 in closed form in terms of the model parameters If surge is too valuable compared to non-surge on average, then cannot build fully IC prices

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Empirical goal: Estimate value of a request

How does accepting a given trip request change a driver’s expected earnings over the next 90 minutes?

Open

90 minutes later

Busy

Receives + accepts trip 𝜐 Observe actual driver earnings

Open

Does not accept request Use nearby driver as counter-factual Find a nearby driver match by checking trips that were recently completed with a nearby destination