SMART Infrastructure Facility was pleased to host Dr Dengji Zhao, a Research Fellow at the University of Southampton, UK as he presented ‘Mechanism Design for Ridesharing’ as part of the SMART Seminar Series on October 16th, 2014.

1. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Mechanism Design for Ridesharing
Dengji Zhao1 Dongmo Zhang2 Enrico Gerding1
Gopal Ramchurn1 Makoto Yokoo3 David Parkes4
Nick Jennings1
1University of Southampton, UK
2University of Western Sydney, Australia
3Kyushu University, Japan
4Harvard University, US
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2. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Ridesharing Example
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3. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Ridesharing Example
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4. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Ridesharing Example
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5. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Ridesharing Example
Questions:
How to arrange the
sharing?
How much should
they pay/receive?
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6. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
History
Began in the 1940s in North
America
Been promoted because of
fuel shortages, air pollution and
traffic congestion
Peaked in the US in 1970 with a
commute mode share of 20.4%
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7. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Public and Private Promotions
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8. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
People are still NOT well motivated!
not going well...
Australia (Queensland) will end ridesharing lanes
The average car carries just 1.6 people
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9. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
What are the obstacles?
Safety and Privacy
Flexibility and Reliability
...
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10. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
What are the obstacles?
Safety and Privacy
Flexibility and Reliability
...
Complicated join procedures
No free market competition!
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11. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
What we can do?
Use Mechanism Design to build ridesharing:
Automated ride matching
Automated (profitable) price setting
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12. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
What we can do?
Use Mechanism Design to build ridesharing:
Automated ride matching
Automated (profitable) price setting
(A -> B, cost: 10)
Driver 1
Exisitng
Ridesharing
Services
Auction
Based
Ridesharing
post trips
Rider 2
(A -> B, cost: 15)
search trips
3
ride arrangement
(A -> B, cost: 10)
Driver
(A -> B, cost: 15)
Rider
post trips
1
ride schedules
1
2
2
post trips
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13. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
What we can do?
Use Mechanism Design to build ridesharing:
Automated ride matching
Automated (profitable) price setting
to answer...
Questions:
How to arrange the sharing?
How much should commuters pay/receive?
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14. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Outline
1 The Model
2 Fixed-price Mechanisms
3 VCG with Reserve Prices
4 Balanced Trade Reduction
5 Conclusion
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15. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Outline
1 The Model
Auction-based Ridesharing
2 Fixed-price Mechanisms
3 VCG with Reserve Prices
4 Balanced Trade Reduction
5 Conclusion
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16. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
System Overview
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17. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
System Overview
Input:
Route map: a graph G = (L;E),
L: stopping points/locations,
E: routes between stopping points,
w(e): time required to travel via route e 2 E.
Commuter i’s private trip/type: i = (ld
i ; la
i ; td
i ; ta
i ; ci ; qi )
ld
i ; la
i 2 L: departure and arrival locations,
td
i ; ta
i : earliest departure and latest arrival time,
ci 2 R+: travel cost to finish the trip,
qi 2 N: extra seats available on the trip.
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18. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
System Overview
Output:
Allocation/Scheduling:
driver: drives and takes riders
rider: shares with drivers
unmatched: goes with the original travel preference
Payments:
driver: receives money
rider: pays money
unmatched: no payment
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19. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
The Goal of the System
Properties of the output:
Minimize the total travel costs (efficiency)
Incentivize participation and against manipulations
commuters never receive negative utility (individual
rationality)
truthfully reporting their trip information is a dominant
strategy (truthfulness)
Deficit control (budget balance)
The system owner should not lose too much money
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20. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
One Solution: Applying VCG Mechanism
One classical solution: VCG
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21. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
One Solution: Applying VCG Mechanism
Vickrey Auction (Second Price Auction)
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22. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
One Solution: Applying VCG Mechanism
Vickrey Auction (Second Price Auction)
Allocation: the agent with the highest valuation wins
Payment: the harm of others caused by the winner
Properties: Efficient, Individual Rational, and Truthful.
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23. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
One Solution: Applying VCG Mechanism
Vickrey-Clarke-Groves (VCG) auction
Efficient (costs minimizing)
Individually rational (agents never lose money)
Truthful (truthfully reporting is the best)
High deficit (m times of the costs saved!)
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24. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
One Solution: Applying VCG Mechanism
Vickrey-Clarke-Groves (VCG) auction
Efficient (costs minimizing)
Individually rational (agents never lose money)
Truthful (truthfully reporting is the best)
High deficit (m times of the costs saved!)
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25. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
One Solution: Applying VCG Mechanism
Vickrey-Clarke-Groves (VCG) auction
Efficient (costs minimizing)
Individually rational (agents never lose money)
Truthful (truthfully reporting is the best)
High deficit (m times of the costs saved!)
Question
How to control deficit?
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26. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Auction-based Ridesharing
Our Solutions (Overview)
We propose...
Fixed-price Mechanisms :
Flexible deficit control (outperforms VCG)
Truthful and individually rational
Very inefficient
VCG with Reserve Prices :
Flexible deficit control (outperforms VCG)
(Partially) truthful and individually rational
Flexible efficiency control
Balanced Trade Reduction :
Flexible deficit control (outperforms VCG)
truthful and individually rational
Flexible efficiency control
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27. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Outline
1 The Model
2 Fixed-price Mechanisms
xfixed (p0; p1)
3 VCG with Reserve Prices
4 Balanced Trade Reduction
5 Conclusion
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28. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
xfixed (p0; p1)
Fixed Payments xfixed (p0; p1)
Given predefined values p0 0 (for riders) and p1 0 (for
drivers), fixed payments are defined
Allocation independent
Allocation dependent
location dependent (e.g. shortest path)
detour dependent
sharing dependent
...
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29. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
xfixed (p0; p1)
Dictatorship Mechanism
Serial Dictatorship Mechanism with fixed payments
1 Predefine the set of (potential) drivers and riders
2 Order potential drivers and riders
3 Maximize drivers’ utility according to the order
4 Each driver/rider gets the fixed payment
Properties
truthful and individually rational
better deficit control than VCG
very inefficient
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30. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
xfixed (p0; p1)
Problems of Non-dictatorship Mechanisms
Case I:
fixedPay = 10
both prefer driving
potential problem for
deterministic mechanisms
Case II:
fixedPay = 1
both prefer riding
potential problem for all
mechanisms
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31. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Outline
1 The Model
2 Fixed-price Mechanisms
3 VCG with Reserve Prices
MVCG(r 0; r 1)
4 Balanced Trade Reduction
5 Conclusion
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32. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
MVCG(r0; r1)
VCG with Two-Sided Reserve PricesMVCG(r 0; r 1)
Predefined reserve prices r 0 0 (for riders) and r 1 0 (for
drivers),
Note: r0 and r1 can be allocation dependent.
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33. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
MVCG(r0; r1)
Properties ofMVCG(r 0; r 1)
MVCG(r 0; r 1) is
truthful iff r 0 r 1. Otherwise, the manipulation
gain is bounded (max(r 1 r 0; max
i (r 1 r 0))).
weakly budget balanced without detour.
Otherwise, deficit is bounded (nd maxr 1 nr r 0).
more efficient as r 0 + r 1 decreases.
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34. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
MVCG(r0; r1)
A Common Feature of the Dictatorship and VCG with
Reserves
The truthfulness is satisfied if
each commuter can only be allocated as one predefined
role (driver or rider) or unmatched.
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35. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Outline
1 The Model
2 Fixed-price Mechanisms
3 VCG with Reserve Prices
4 Balanced Trade Reduction
McAfee’s Trade Reduction
Balanced Trade Reduction
5 Conclusion
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36. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
McAfee’s Trade Reduction
McAfee’s Trade Reduction (1992)
McAfee’s reduction: increase VCG payments via reducing
efficiency
53
79
85
90
94
98
113
121
125
120
112
91
82
82
69
37
sellers/
drivers
buyers/
riders
VCG payments:
Riders: 90
Drivers: 91
Deficit: 4
McAfee’s payments:
Riders: 91
Drivers: 90
No deficit!
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37. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
McAfee’s Trade Reduction
McAfee’s Reduction is NOT Truthful in Ridesharing
McAfee’s trade reduction is NOT truthful in ridesharing
because:
a commuter who can be allocated as either driver or rider
might manipulate/switch!
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38. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Balanced Trade Reduction
Balanced Trade Reduction (BTR)
VCG payment for a buyer
vb
xvcg
xvcg
i i ^i vs
i
McAfee’s payment for a buyer
vb
i (xvcg
i (^xvcg
i + 1) vs
i + 2)
Balanced Trade Reduction payment for a buyer
vb
i (xvcg
i (^xvcg
i + ) vs
i + )
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39. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Balanced Trade Reduction
Balanced Trade Reduction (BTR)
VCG payment for a buyer
vb
xvcg
xvcg
i i ^i vs
i
McAfee’s payment for a buyer
vb
i (xvcg
i (^xvcg
i + 1) vs
i + 2)
Balanced Trade Reduction payment for a buyer
vb
i (xvcg
i (^xvcg
i + ) vs
i + )
Properties of BTR:
Truthful, Individual Rational, almost Efficient, but has
Deficit.
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40. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Outline
1 The Model
2 Fixed-price Mechanisms
3 VCG with Reserve Prices
4 Balanced Trade Reduction
5 Conclusion
Done and ToDo
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41. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Done and ToDo
What is NEW?
The first comprehensive ridesharing model studied from a
pure game-theoretic point of view.
Auction-based ridesharing system incentivizing
participation.
Flexible deficit control rather than completely remove
deficit.
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42. The Model Fixed-price Mechanisms VCG with Reserve Prices Balanced Trade Reduction Conclusion
Done and ToDo
Future Work
Tradeoff between deficit and efficiency (theoretically or
simulations).
The problem of finding optimal schedules is
computationally hard (optimal in range).
Allow agents to submit trips dynamically over time (online
mechanism design).
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