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- © Hajime MizuyamaA Prediction Market Gamefor Route Selection under UncertaintyHajime Mizuyama, Shuhei Torigai and Michiko AnseDept. of Industrial and Systems EngineeringAoyama Gakuin Universitymizuyama@ise.aoyama.ac.jpISAGA 2013 @ Stockholm 24/June/2013
- © Hajime MizuyamaRoute 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 arcWhat if information is limited?Research background© Hajime MizuyamaStartGoal
- © Hajime Mizuyama• For example, after the Tohoku earthquake, relief goodsshould be delivered to the disaster-stricken area.• However, the disaster was so severe that the conditionof the road network was significantly altered.• As a result, not only solving a shortest path problembut also reformulating the problem itselfbecame necessary.Research background© Hajime MizuyamaStartGoalCrowdsourcing approachfor information gathering
- © Hajime MizuyamaFuturesmarketPrediction market framework for crowdsourcingProblemSolutionPredictionsecurityMarketprice
- © Hajime Mizuyama• Formulate a composite route selection problem under uncertainty, wherereformulating a shortest path problem and resolving it need to be dealt withsimultaneously.• Develop a prototype prediction market game, which is suitable foraddressing the composite route selection problem through crowdsourcingapproach for information gathering.• Experimentally apply the proposed game to a simple real-life problem, andstudy how it works.Research objective
- © Hajime Mizuyama• Research background and objective• Problem formulation• Game design• Gaming experiments• Game results and discussion• ConclusionsAgenda
- © Hajime Mizuyama• The structure of the route selection problem can be captured as an ordinalshortest path problem, that is, the topology of the available road network isknown and is modeled as a directed graph G = (V, A).• The start and goal nodes are represented as vO and vD (in V), respectively, andthe 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 itsdistribution is unknown to the decision maker.• Since the length of each arc is a random variable, which route is the shortestmay also be probabilistic.• Thus, the problem is to estimate for each route rj (in R) the probability that itwill be the shortest.Route selection problem under uncertainty
- © Hajime Mizuyama• Research background and objective• Problem formulation• Game design• Gaming experiments• Game results and discussion• ConclusionsAgenda
- © Hajime MizuyamaAn ordinal prediction market settingDouble auction marketBid and ask offersMarket prices= Probabilitiesof beingelectedCandidateACandidateBCandidateCWTA securitiesA fixed posteriorpayoff only forthe electedcandidatePrediction market game design: Security design Market design
- © Hajime MizuyamaRoute security:• A fixed posterior payoff only for the one corresponding to the shortest pathidentified by a post-hoc evaluation• Straightforward to compare among possible routes• Not suitable for capturing dispersed local knowledgeArc 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 knowledgeSecurity design
- © Hajime Mizuyama• Since double auction mechanism is not suitable for a thin market, theproposed game utilizes a computerized central market maker system.• More specifically, it uses the logarithmic market scoring rule (LMSR), which isone of the most widely-used market maker algorithms for prediction markets.• LMSR handles transactions of a set of prediction securities corresponding tomutually 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 istreated as a bundle of the route securities containing the arc.Market design
- © Hajime MizuyamaOutline of proposed gameLMSR for route securitiesArc securitiesA fixed posteriorpayoff only forthose included inthe shortest path Possible routesare comparedaccording tothe prices ofroute securitiesTrading arc securitiesEach arc security is deemed asa bundle of route securities.
- © Hajime Mizuyama• Research background and objective• Problem formulation• Game design• Gaming experiments• Game results and discussion• ConclusionsAgenda
- © Hajime MizuyamaExample road networkvOvDa1a12a10a9a8a7a6a4a5a3a2a11Train stationSchool gateHC: High congestion situationLC: Low congestion situation
- © Hajime MizuyamaPossible routes from train station to school gateRoute Included arcs Route Included arcsr1 a1 - a8 - a11 r6 a2 - a4 - a7 - a10 - a12r2 a1 - a8 - a12 r7 a2 - a4 - a5 - a8 - a11r3 a2 - a6 - a9 - a10 - a11 r8 a2 - a4 - a5 - a8 - a12r4 a2 - a6 - a9 - a10 - a12 r9 a3 - a9 - a10 - a11r5 a2 - a4 - a7 - a10 - a11 r10 a3 - a9 - a10 - a11
- © Hajime MizuyamaResults of walking experimentsRouteLC situation HC situationMean(s)Std. dev.(s)Prob.(%)Mean(s)Std. dev.(s)Prob.(%)r1 661 54 0.2 671 61 1.0r2 592 56 1.4 631 67 3.5r3 491 22 5.3 627 66 3.7r4 453 42 42.4 579 61 9.4r5 533 50 5.0 560 56 13.2r6 470 45 27.4 529 56 26.0r7 550 49 3.0 548 58 17.7r8 479 31 15.3 545 81 25.2r9 651 31 0.0 686 35 0.1r10 582 14 0.0 652 39 0.3
- © Hajime Mizuyama• 18 undergraduate students are grouped into team A, B and C.• At the beginning of each market session, every team member was providedan initial endowment of P$1000.• Further, five pieces of every arc security were also given only to the membersof 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 thesession 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 ofa market session to a unit of each arc security contained in the route havingthe highest probability of being the shortest.• The winner of the game was the player having the highest posterior wealthincluding the payoff.Experimental settings
- © Hajime MizuyamaA market game session
- © Hajime MizuyamaA market game session
- © Hajime MizuyamaFinal price of each route securityRouteLC situation HC situationTeam A Team B Team C Team A Team B Team Cr1 6.4 6.0 1.6 8.8 7.6 4.6r2 8.3 7.6 4.4 11.0 8.0 5.6r3 12.7 12.8 11.8 8.8 8.9 6.8r4 16.4 16.3 31.5 11.1 9.2 8.3r5 8.7 9.5 5.7 9.0 12.2 13.9r6 11.2 12.1 15.2 11.4 12.7 17.1r7 7.6 9.0 3.6 10.0 13.1 16.1r8 9.9 11.5 9.6 12.5 13.7 19.9r9 8.2 6.7 4.5 7.7 7.1 3.5r10 10.6 8.5 12.1 9.7 7.4 4.3
- © Hajime MizuyamaTheoretical prices vs. market prices (LC situation)0 10 20 30 4005101520253035Theoretical PriceMarketPrice Team A (Cor.coef.=0.80)Team B (Cor.coef.=0.86)Team C (Cor.coef.=0.89)
- © Hajime MizuyamaTheoretical prices vs. market prices (HC situation)0 10 20 30 4005101520253035Theoretical PriceMarketPrice Team A (Cor.coef.=0.70)Team B (Cor.coef.=0.95)Team C (Cor.coef.=0.98)
- © Hajime Mizuyama• A route selection problem under uncertainty is formulated, which is anordinal shortest path problem but the length of each arc is a random variablefollowing an unknown distribution.• A prediction market game is proposed for addressing the route selectionproblem under uncertainty and a simple prototype platform for the game isdeveloped.• The proposed gaming approach is tested on the platform, and it is confirmedthat this approach can produce satisfactory results.• Future research directions include extending the approach applicable to alarge-scale problem, incorporating topological uncertainty, and designingappropriate incentives for participation.Conclusions
- Thank you for your kind attention!Questions and comments are welcome.