1. © Hajime Mizuyama
A Prediction Market Game
for Route Selection under Uncertainty
Hajime Mizuyama, Shuhei Torigai and Michiko Anse
Dept. of Industrial and Systems Engineering
Aoyama Gakuin University
mizuyama@ise.aoyama.ac.jp
ISAGA 2013 @ Stockholm 24/June/2013

2. © Hajime Mizuyama
Route selection decisions need to be made in various situations.
– Product delivery
– Train and bus travel
– Manufacturing process planning, etc.
They are often treated as a shortest path problem.
– Topology of road network
– Length of each arc
What if information is limited?
Research background
© Hajime Mizuyama
Start
Goal

3. © Hajime Mizuyama
• For example, after the Tohoku earthquake, relief goods
should be delivered to the disaster-stricken area.
• However, the disaster was so severe that the condition
of the road network was significantly altered.
• As a result, not only solving a shortest path problem
but also reformulating the problem itself
became necessary.
Research background
© Hajime Mizuyama
Start
Goal
Crowdsourcing approach
for information gathering

4. © Hajime Mizuyama
Futures
market
Prediction market framework for crowdsourcing
Problem
Solution
Prediction
security
Market
price

5. © Hajime Mizuyama
• Formulate a composite route selection problem under uncertainty, where
reformulating a shortest path problem and resolving it need to be dealt with
simultaneously.
• Develop a prototype prediction market game, which is suitable for
addressing the composite route selection problem through crowdsourcing
approach for information gathering.
• Experimentally apply the proposed game to a simple real-life problem, and
study how it works.
Research objective

6. © Hajime Mizuyama
• Research background and objective
• Problem formulation
• Game design
• Gaming experiments
• Game results and discussion
• Conclusions
Agenda

7. © Hajime Mizuyama
• The structure of the route selection problem can be captured as an ordinal
shortest path problem, that is, the topology of the available road network is
known and is modeled as a directed graph G = (V, A).
• The start and goal nodes are represented as vO and vD (in V), respectively, and
the set of possible routes or paths from vO to vD is denoted as R.
• The length of each arc ai (in A) is an uncertain random variable and its
distribution is unknown to the decision maker.
• Since the length of each arc is a random variable, which route is the shortest
may also be probabilistic.
• Thus, the problem is to estimate for each route rj (in R) the probability that it
will be the shortest.
Route selection problem under uncertainty

8. © Hajime Mizuyama
• Research background and objective
• Problem formulation
• Game design
• Gaming experiments
• Game results and discussion
• Conclusions
Agenda

9. © Hajime Mizuyama
An ordinal prediction market setting
Double auction market
Bid and ask offers
Market prices
= Probabilities
of being
elected
Candidate
A
Candidate
B
Candidate
C
WTA securities
A fixed posterior
payoff only for
the elected
candidate
Prediction market game design:
 Security design
 Market design

10. © Hajime Mizuyama
Route security:
• A fixed posterior payoff only for the one corresponding to the shortest path
identified by a post-hoc evaluation
• Straightforward to compare among possible routes
• Not suitable for capturing dispersed local knowledge
Arc security:
• A fixed posterior payoff only for those included in the shortest path
• Not straightforward to compare among possible routes
• Suitable for capturing dispersed local knowledge
Security design

11. © Hajime Mizuyama
• Since double auction mechanism is not suitable for a thin market, the
proposed game utilizes a computerized central market maker system.
• More specifically, it uses the logarithmic market scoring rule (LMSR), which is
one of the most widely-used market maker algorithms for prediction markets.
• LMSR handles transactions of a set of prediction securities corresponding to
mutually exclusive and collectively exhaustive possible events.
• Thus, it cannot be directly applied to arc securities.
• LMSR is run for route securities behind the scenes, and each arc security is
treated as a bundle of the route securities containing the arc.
Market design

12. © Hajime Mizuyama
Outline of proposed game
LMSR for route securities
Arc securities
A fixed posterior
payoff only for
those included in
the shortest path Possible routes
are compared
according to
the prices of
route securities
Trading arc securities
Each arc security is deemed as
a bundle of route securities.

13. © Hajime Mizuyama
• Research background and objective
• Problem formulation
• Game design
• Gaming experiments
• Game results and discussion
• Conclusions
Agenda

14. © Hajime Mizuyama
Example road network
vO
vD
a1
a12a10
a9
a8
a7
a6
a4
a5
a3
a2
a11
Train station
School gate
HC: High congestion situation
LC: Low congestion situation

15. © Hajime Mizuyama
Possible routes from train station to school gate
Route Included arcs Route Included arcs
r1 a1 - a8 - a11 r6 a2 - a4 - a7 - a10 - a12
r2 a1 - a8 - a12 r7 a2 - a4 - a5 - a8 - a11
r3 a2 - a6 - a9 - a10 - a11 r8 a2 - a4 - a5 - a8 - a12
r4 a2 - a6 - a9 - a10 - a12 r9 a3 - a9 - a10 - a11
r5 a2 - a4 - a7 - a10 - a11 r10 a3 - a9 - a10 - a11

16. © Hajime Mizuyama
Results of walking experiments
Route
LC situation HC situation
Mean
(s)
Std. dev.
(s)
Prob.
(%)
Mean
(s)
Std. dev.
(s)
Prob.
(%)
r1 661 54 0.2 671 61 1.0
r2 592 56 1.4 631 67 3.5
r3 491 22 5.3 627 66 3.7
r4 453 42 42.4 579 61 9.4
r5 533 50 5.0 560 56 13.2
r6 470 45 27.4 529 56 26.0
r7 550 49 3.0 548 58 17.7
r8 479 31 15.3 545 81 25.2
r9 651 31 0.0 686 35 0.1
r10 582 14 0.0 652 39 0.3

17. © Hajime Mizuyama
• 18 undergraduate students are grouped into team A, B and C.
• At the beginning of each market session, every team member was provided
an initial endowment of P$1000.
• Further, five pieces of every arc security were also given only to the members
of team C to make it easier for them to sell arc securities.
• No preset limit was imposed on the length of a market session, but the
session was terminated when no one wanted to conduct further transactions.
• The amount of posterior payoff was set to P$100, and was given at the end of
a market session to a unit of each arc security contained in the route having
the highest probability of being the shortest.
• The winner of the game was the player having the highest posterior wealth
including the payoff.
Experimental settings

18. © Hajime Mizuyama
A market game session

19. © Hajime Mizuyama
A market game session

20. © Hajime Mizuyama
• Research background and objective
• Problem formulation
• Game design
• Gaming experiments
• Game results and discussion
• Conclusions
Agenda

21. © Hajime Mizuyama
Final price of each route security
Route
LC situation HC situation
Team A Team B Team C Team A Team B Team C
r1 6.4 6.0 1.6 8.8 7.6 4.6
r2 8.3 7.6 4.4 11.0 8.0 5.6
r3 12.7 12.8 11.8 8.8 8.9 6.8
r4 16.4 16.3 31.5 11.1 9.2 8.3
r5 8.7 9.5 5.7 9.0 12.2 13.9
r6 11.2 12.1 15.2 11.4 12.7 17.1
r7 7.6 9.0 3.6 10.0 13.1 16.1
r8 9.9 11.5 9.6 12.5 13.7 19.9
r9 8.2 6.7 4.5 7.7 7.1 3.5
r10 10.6 8.5 12.1 9.7 7.4 4.3

22. © Hajime Mizuyama
Theoretical prices vs. market prices (LC situation)
0 10 20 30 40
05101520253035
Theoretical Price
MarketPrice Team A (Cor.coef.=0.80)
Team B (Cor.coef.=0.86)
Team C (Cor.coef.=0.89)

23. © Hajime Mizuyama
Theoretical prices vs. market prices (HC situation)
0 10 20 30 40
05101520253035
Theoretical Price
MarketPrice Team A (Cor.coef.=0.70)
Team B (Cor.coef.=0.95)
Team C (Cor.coef.=0.98)

24. © Hajime Mizuyama
• Research background and objective
• Problem formulation
• Game design
• Gaming experiments
• Game results and discussion
• Conclusions
Agenda

25. © Hajime Mizuyama
• A route selection problem under uncertainty is formulated, which is an
ordinal shortest path problem but the length of each arc is a random variable
following an unknown distribution.
• A prediction market game is proposed for addressing the route selection
problem under uncertainty and a simple prototype platform for the game is
developed.
• The proposed gaming approach is tested on the platform, and it is confirmed
that this approach can produce satisfactory results.
• Future research directions include extending the approach applicable to a
large-scale problem, incorporating topological uncertainty, and designing
appropriate incentives for participation.
Conclusions

26. Thank you for your kind attention!
Questions and comments are welcome.