Collaboration and Shared Plans in the Open World:Studies of Ridesharing

Ece Kamar ∗

SEAS, Harvard UniversityCambridge, MA 02138

kamar@eecs.harvard.edu

Eric HorvitzMicrosoft Research

Redmond, WA 98052horvitz@microsoft.com

AbstractWe develop and test computational methods forguiding collaboration that demonstrate how sharedplans can be created in real-world settings, whereagents can be expected to have diverse and varyinggoals, preferences, and availabilities. The meth-ods are motivated and evaluated in the realm ofridesharing, using GPS logs of commuting data.We consider challenges with coordination amongself-interested people aimed at minimizing the costof transportation and the impact of travel on theenvironment. We present planning, optimization,and payment mechanisms that provide fair and ef-ficient solutions to the rideshare collaboration chal-lenge. We evaluate different VCG-based paymentschemes in terms of their computational efficiency,budget balance, incentive compatibility, and strat-egy proofness. We present the behavior and anal-yses provided by the ABC ridesharing prototypesystem. The system learns about destinations andpreferences from GPS traces and calendars, andconsiders time, fuel, environmental, and cognitivecosts. We review how ABC generates rideshareplans from hundreds of real-life GPS traces col-lected from a community of commuters and reflectabout the promise of employing the ABC methodsto reduce the number of vehicles on the road, thusreducing CO2 emissions and fuel expenditures.

1 IntroductionWe investigate challenges with the generation of efficientcollaborative plans for self-interested people based on theiravailabilities and preferences, and with providing fair incen-tives to promote collaboration. We frame and motivate thedevelopment of methods with the real-world challenge ofgenerating shared transportation plans, referred to commonlyas ridesharing. Rideshare plan generation is an interestingand representative open-world collaboration problem becauseof the varying goals, diverse preferences, and changing lo-cations and availabilities of actors. Beyond the intriguing

∗Ece Kamar performed this research during an internship at Mi-crosoft Research.

technical challenges, the pursuit of effective rideshare plangeneration is also motivated by the potential value of im-plementing wide-scale ridesharing for the environment andeconomy. Transportation is a significant source of CO2 emis-sions [e Sustainability Initiative, 2008]; ridesharing has beenproposed as a promising means for reducing these emissionsas well as fuel expenditures. Although making use of unfilledseats in cars can deliver personal and more global value, par-ticipants in a carpool can incur costs with ridesharing, includ-ing fuel and time costs associated with the lengthening of acommute containing new waypoints, and a shifting of the de-parture and arrival times to match the needs of others.

We present a formal methodology for generating idealridesharing plans for a community of users. We pursue incen-tive mechanisms that provide fair and efficient solutions whilerespecting the privacy of users and promoting truthful behav-ior. The coordination machinery generalizes to other settingswhere agents need to collaborate on joint plans to minimizetheir cumulative cost, and obtain fair payments as incentives.Beyond usage in online systems for generating batch and real-time rideshare plans, the methods provide tools for exploringthe influence of changing parameters, such as the cost of fueland time and numbers of participants, on the overall efficien-cies and savings achieved.

We shall discuss several phases of analysis for construct-ing collaborative plans for ridesharing, including the acquisi-tion of changing user costs and preferences for ridesharing,the solution of computationally expensive optimization prob-lems and the use of VCG-based payment schemes in a dy-namic setting. We explore different mechanism design ideasand discuss the goals of computational efficiency, budget bal-ance, incentive compatibility, and strategy proofness, whileaddressing the computational limitations of a dynamic mech-anism. We review the operation of a prototype and experi-mental platform called the Agent-Based Carpool (ABC) sys-tem. We describe how ABC generates rideshare plans fromhundreds of real-life GPS traces, collected from a commu-nity of commuters over five years. The empirical results in-dicate significant reductions on number of commutes and ontotal cost of transportation, and show promise for generatingefficiency by bringing self-interested agents together. In ad-dition, they highlight challenges and tradeoffs that arise fromthe coordination of self-interested agents in real-life domains.

There has been growing interest in the use of the web and

computing methods in assisting with ridesharing. A numberof online rideshare services1 offer users varied experiencesfrom simple to complicated. Nuride, Zimride, Craigslist andmailing groups provide social networks where users can man-ually arrange carpools. More sophisticated ridesharing ser-vices such as iCarpool and CarpoolWorld help users with on-line trip matching. These services also motivate users to car-pool with mile-based rewards, or interfaces for negotiation onpayments. The systems typically serve as platforms that bringusers together, rather than as active mechanisms that generaterideshare plans and provide fair payments.

Altruism and reciprocity have been proposed as strategiesto explain and promote cooperation among people when theyinteract repeatedly [Bowles and Gintis, 2005]. However, indynamic domains we consider in this work, collaborative car-pool plans may change with respect to changing preferencesof users (e.g., trip start times, meeting schedules, cost of de-lay), and drivers may be paired with different set of passen-gers each day. Therefore, cooperation strategies such as al-truism and reciprocity that require continuous interactions arenot typically valid for dynamic domains such as ours.

Coalescing rational agents into groups of participants inrideshare plans is similar to the initial-commitment decisionproblem (ICDP) proposed by [Hunsberger and Grosz, 2000],as both problems aim to determine the set of tasks that agentsneed to commit in a collaboration. The methods employedin ABC system are an extension to prior work on ICDP as apayment mechanism is included, which provides a rationaleand incentives for self-interested agents to collaborate.

Several previous studies on set-cover optimization prob-lems focus on mechanism design for cost sharing [Devanur etal., 2005; Li et al., 2005]. The cost sharing problem focuseson dividing the cost of a service among self-interested agentsin a fair manner, where the cost is independent of agents’preferences. The optimization used in ABC makes use ofgreedy optimization procedures similar to the approach takenin the earlier set-cover optimization efforts. However, thepayment mechanisms employed in the past are not suitablefor collaboration among self-interested agents. We don’t havea distinction between service providers and receivers, and thecost is not independent of agents’ preferences.

Mechanism design has been applied to the coordination ofself-interested robots in sequential decision-making scenar-ios [Cavallo et al., 2006]. Our work differs from the priorwork in that both the joint plans and payments are based oncombinations of dynamic and changing preferences of peopleabout their daily habits including time, fuel, cognitive costsand travel preferences. We also present detailed analysis ofthe optimization and payment mechanisms with respect to thecomputational issues with real-life data in a dynamic domain.

2 Methodology and ArchitectureComputing ideal ridesharing plans is a challenging problemas the solution must consider the varied and dynamicallychanging preferences of self-interested agents, must providecompelling and fair incentives, and must be easy to use. The

1www.nuride.com, www.carpoolworld.com, www.zimride.com,sfbay.craigslist.org/sfo/rid/, www.icarpool.com

ABC prototype addresses these challenges by creating per-sonalized rideshare plans while minimizing the cumulativecost of transportation. The system has three main componentsthat embody separate but interrelated reasoning methodolo-gies: a user-modeling component that accesses and repre-sents the preferences of agents, an optimization componentthat generates collaborative rideshare plans, and a paymentcomponent that provides incentives to agents to collaborate.

The user-modeling component is responsible for identify-ing the preferences of agents about their desired trips, andfor passing the preferences into the optimization and paymentcomponents. It gathers information about agents’ individualcommute plans, including their origin, destination, timing ofa trip, and preferences about a return trip. A destination an-alyzer accesses or infers the intended destination of a mo-bile user under uncertainty [Krumm and Horvitz, 2006]. Toperform cost-benefit analysis of a ridesharing plan, the user-modeling component models agent-specific costs for driving,delaying a trip, diverting an ideal route to pick up or dropoff other agents, and changing stop points. Capturing thesecosts in a dynamic manner is crucial for the success of theridesharing system, as the system needs to adapt to differentand changing preferences of agents. For example, an agentmay be willing to wait and pick up other agents on the waywhen the cost of time is low, but not on a rainy day when thecost of time is high.

Time is an important resource and is one of the ma-jor factors influencing the cost of different commute plans.The user-modeling component employs a probabilistic time-cost model. The model considers as input the time of day,day of week, and sets of attributes about agents’ commit-ments drawn from an online appointment book. Probabilis-tic models for the cost of time and for the commitment toattend events are learned from user annotated training datavia a machine-learning procedure based on Bayesian struc-ture search. Similar predictive models of the cost of timeand meeting commitments have been used in other applica-tions, including mobile opportunistic planning [Horvitz et al.,2007; Kamar et al., 2008], meeting coordination [Horvitz etal., 2002] and the triaging and routing of communications[Horvitz et al., 2005]. See [Horvitz et al., 2005] for addi-tional details about the machine learning and reasoning aboutthe cost of time in different settings and the evaluated perfor-mance of the predictive models of the context-sensitive costof time. For each agent, the user modeling component con-structs a time-cost function T to estimate the cost of the timespent travelling between the start time (ts) and end time (te)of a trip, and the additional cost for delaying the start timeof a rideshare trip from the initial start time tos to ts. T iscaptured with respect to the nearest deadlines drawn from theagent’s calendar. Given that the set of calendar items fall be-tween [ts, te] is M , m ∈ M is a calendar item, the start timeof m is tms , the end time of m is tme , cn is the minute time costfor travelling, cm is the additional cost for missing a minuteof m, cd is the minute cost for delay; T is defined as,

T (ts, te) = ((te − ts)× cn) + (|ts − tos| × cd)+(

∑

m∈M

(min(tme , te)−max(tms , ts))× cm)

3 Rideshare OptimizationThe optimization component groups agents together and gen-erates a collection of rideshare plans that maximizes the ef-ficiency of transportation. The component acquires privateuser preferences from the user modeling component, com-bines them with global contexts to capture the collaborativevalue of a rideshare plan. The optimization component hasthe following properties that make it difficult for agents tofind out about other agents in the system and thus collude inthe mechanism; the component combines multiple user pref-erences and contextual factors to determine the best possibleplan, agents do not get to know about other users’ preferencesor rideshare plans that they are not involved in. The optimiza-tion component takes in the set of individual desired commuteplans as inputs and solves two difficult optimization prob-lems to generate a collection of collaborative rideshare plans.The two optimizations are: (1) generating rideshare plansfor groups of agents and (2) clustering agents into ridesharegroups (see Figure 1).

3.1 Rideshare PlansChoosing the best possible rideshare plan with respect toagent preferences is a large search problem where the sys-tem explores possible combinations of trip start times, stoporderings, stop locations, trip durations, and possible routesamong stop points to generate a plan with highest possiblecumulative value. Let P be the set of all agents in ridesharesystem, S ⊆ P a rideshare group, C(S) the universe of allpossible rideshare plans for S. A rideshare plan Ci ∈ C(S) isdefined by the following attributes:• S = {ph, . . . , pq}, the set of agents of the rideshare

group; pd ∈ S, the assigned driver for the rideshare plan;S−d = S \ {pd}.

• L−d = {`h,s, `h,e, . . . , `q,s, `q,e}, the set of start\end(stop) locations of agents in S−d, where pi’s start loca-tion is `i,s, the end location is `i,e. For all pi ∈ S−d,`i,s and `i,e are located in a radius of `o

i,s and `oi,e – the

initial start\end locations for pi’s individual commuteplan. L, the complete set of start\end locations, is thecombination of L−d with the start\end locations of pd:L = L−d

⋃{`d,s, `d,e}, where `d,s = `od,s , `d,e = `o

d,e.• Θ−d, the commute chain excluding pd, is any order-

ing of L−d such that for all pi ∈ S−d, index(`i,s) <index(`i,e) (i.e., any agent’s start location precedes theend location in Θ−d). Θ = `d,s ◦Q−d ◦ `d,e is the com-mute chain for S.

• ts, the start time of the rideshare plan. t(l), the sched-uled time of stop location l is defined as below, where∆t(`j , `j+1) is the estimated travel duration betweentwo consecutive stop locations `j , `j+1 ∈ Θ:

t(`) =

ts ` = `d,s

ts +∑

j<index(`)

∆t(`j , `j+1) otherwise

3.2 Value of Shared PlansAlthough reduction in fuel costs and personal or organiza-tional (e.g., per the goals of an employer) goals of reduc-ing CO2 emissions from vehicles are the primary motivations

for bringing self-interested agents to collaborate in rideshareplans, the additional time and travel required for adding newstops to a trip, or having fewer numbers of agents driving inheavy traffic can play an important role in the willingness ofagents to participate. We define a personal inconvenience costthat captures several agent-specific cost factors. The personalinconvenience factors are composed to yield the cumulativevalue of a rideshare plan.

(a) (b)

(c) (d)

Figure 1: ABC rideshare optimization. (a) Input of individualcommute plans. The initial segments of the individual plansare drawn as blue lines originating from the start positions ofagents indicated by blue dots. Each start position is labeledby the username and original start time. (b) Rideshare planoptimization. Individual plans acquired from four users areshown by top left. Middle right images display three differentrideshare plans generated for users. The economical analysisof a rideshare plan in terms of fuel, time, cognitive costs andCO2 emissions is illustrated on the bottom. (c) Ridesharegroup optimization. Users assigned to the same ridesharegroups are labeled with the same color. (d) Rideshare plansgeneration. Shared transportation plans are drawn with bluelines. Each circle represents the rideshare group that a useris assigned to, and is labeled with the username, and with theupdated and original start times.

A model for the cost of personal inconvenience combinesthe cost of a lengthening of the duration of the commute andof shifts in leaving and arrival times with gains in the sav-ings of fuel and reduction in the cognitive costs of drivinga vehicle, to yield an estimate of the net value of an agentbecoming associated with a trip. The user modeling compo-

nent provides the probabilistic time-cost function, Ti(ts, te).The fuel cost in dollars for one mile is represented as cg .The inconvenience model combines the input from the usermodeling component with traffic prediction services and pub-lic contexts (e.g., daily events that may affect the traffic) toconstruct a cognitive cost model for an agent. CCi(`s, `e)represents the predicted cognitive cost of pi for driving be-tween the given stops. The optimization engine makes calls toMicrosoft Mappoint services to estimate the travel duration.∆t(`i, `j) represents the duration of travel between stops `i

and `j , whereas ∆d(`i, `j) represents the distance to be trav-elled between these stops.

The initial inconvenience cost of agent pi, PCo(pi), rep-resents the cost for following the individual trip that wouldbe created between initial start\end locations of pi in the ab-sence of ridesharing, where the start time of the individualtrip is toi,s.

PCo(pi) = Ti(toi,s, toi,e) + ∆d(`o

i,s, `oi,e)× cg +

CCi(`oi,s, `

oi,e)

toi,e = toi,s + ∆t(`oi,s, `

oi,e)

A fuel and cognitive cost is incurred if an agent is assignedas the driver in a given trip. Let `j , `j+1 ∈ L be consecutivestop locations in commute chain Θ, PC(pd, C) is the incon-venience cost of the driver for rideshare plan C.

PC(pd, C) = Td(t(`d,s), t(`d,e))+∑

`j ,`j+1

(∆d(`j , `j+1)× cg + CCd(`j , `j+1))

The passengers of a rideshare are only subject to time costsfor the period of time for travel between their scheduled startand end locations. PC(pi, C) is the inconvenience cost ofpassenger pi ∈ S−d for rideshare plan C.

PC(pi, C) = Ti(t(`i,s), t(`i,e))

vi(C) represents the value of agent pi for rideshare planC. The cumulative value of a rideshare plan, V (C), repre-sents the value of agents in rideshare plan C for switching tocollaborative plan C from their individual plans.

vi(C) = PCo(pi)− PC(pi, C)

V (C) =∑

pi∈S

vi(C)

Before leaving our discussion of preferences, we note thatthere are subtle, yet potentially powerful psychological andsocial costs and benefits associated with sharing rides withothers in the open world. We see an opportunity to assessand smoothly integrate key psychosocial factors as additionalcosts into the optimization used for generating plans. Forinstance, participants can be offered the option of providingpreference functions that yield estimates of the cost of travel-ing with one or more people based on an established reputa-tion, and on social or organizational relationships. As exam-ples, preferences can be captured with utility functions that

specify the costs with including people in a shared plan thatare related to the participant via different types of organiza-tional links or via increasing graph distances in a social net-work. Such additional costs would likely influence individualobjective functions, and thus the overall behavior of the sys-tem, leading to modifications in the rideshare plans generatedas compared to the output system that does not consider thepsychosocial issues.

3.3 Plan Optimization as SearchRideshare plan optimization seeks to identify the sharedtransportation plan for a group of agents S with the high-est cumulative value. This optimization problem is a searchproblem over the universe of rideshare plans C(S) availablefor S, where the search dimensions of C(S) are the set of pos-sible commute chains, set of possible stop locations for thepassengers, trip start times, and potential routings betweenstop points. The optimization component performs geospatialsearch over the feasible paths that satisfy the constraints of arideshare plan for S. Given the start\end locations of the as-signed driver, the optimizer considers sets of updated routesby adding potential passenger stop points as waypoints andperforming A∗ search. The set of potential passenger stoppoints are selected from a radius around the initial stop pointsof the passenger. The magnitude of the radius is limited by themaximum distance the passenger is willing to diverge fromthe initial stop location to have a more efficient rideshare.The engine searches for the start time of the rideshare planthat minimizes the total cost.

The plan optimizer selects the plan C∗(S) that offers themaximum cumulative value to agent set S, among all pos-sible plans C(S). It provides C∗(S) to the rideshare groupoptimizer.

C∗(S) = arg maxCj∈C(S)

V (Cj)

3.4 Group Assignment as Set CoverGiven a set of agents P in the rideshare system, the ridesharegroup optimization finds the set of subset of P that covers allagents in P by offering the highest cumulative value. Thus,this optimization is identical to the well-known NP-hard set-cover problem.

Let us consider a set of agents, P = {p1, . . . , pn} will-ing to collaborate in a rideshare system. k is the capacity ofa single vehicle, thus the maximum size of a collaborativerideshare group. A set cover for SCi = {Sh, . . . , Sm} foragent set P is a set of subsets of P , such that for all subsetsSj ; |Sj | ≤ k,

⋃Sj∈SCi

Sj = P , and for any Sj , Sk ∈ SCi

Sj

⋂Sk = ∅. Thus, a set cover SCi in rideshare system rep-

resents a collection of rideshare groups, and their best pos-sible rideshare plans that cover all agents in the ridesharingsystem without exceeding the capacity of a transportation ve-hicle. SC(P) = {SC1, . . . , SCr} is defined to be the uni-verse of all set covers for set of agents P .

We define a valuation function V (Sj), which correspondsto the value generated by the best possible rideshare plan forbringing agents Sj together. The value of a set cover SCi,which is also a collective rideshare plan for P is calculated asgiven below:

V (Sj) ={

0 |Sj | ≤ 1V (C∗(Sj)) otherwise

V (SCi) =∑

Sj∈SCi

V (Sj)

A set-cover solver returns the optimal set cover SC∗ =arg maxSCi∈SC(P) V (SCi). The dynamic, open-world na-ture of the domain requires the optimization to run efficientlybecause agents may unexpectedly arrive, leave, or changepreferences which may result in running the optimizationmultiple times. However, optimal set cover solver takes ex-ponential time in practice. Additionally, the optimizationcalls expensive online traffic prediction and routing servicesto evaluate the value of each set cover which makes the opti-mization more expensive. Thus, the optimal set-cover solveris infeasible to apply in open-world settings, and we imple-ment an approximate, greedy set-cover algorithm to generatethe rideshare groups [Li et al., 2005].

The rideshare optimization system ensures that norideshare group is worse off by engaging in the process. Therideshare group generator includes single-item subsets as wellas rideshare groups in the set-cover optimization, thus selectsindividual (initial) trips for some of the agents rather thanassigning them into carpools should no beneficial rideshareplan be available. Thus, any rideshare group generated bythe optimizers offers non-negative cumulative utility to theagents. However, ensuring non-negative utility does not guar-antee individual rationality or fairness between agents in therideshare system. The system may incur additional coststo the assigned driver for a group while generating benefitfor the other passengers. In the next section, we investigatepayment mechanisms that can fairly divide the collaborativebenefit generated by the rideshare optimization componentamong participants.

4 Mechanism Design for CollaborationThe payment mechanism is a crucial component of ABC’soperations as it promotes collaboration among people, anddirectly influences the user behavior and the efficiency of thesystem. Sharing fuel costs among passengers is a simple butwidely used payment mechanism in ridesharing. Howeverthis simple payment scheme is not suitable for a personalizedridesharing system, because it does not consider varying usercosts in payment calculation. Using such a payment schemein ABC would make the system vulnerable to deceptive re-porting of needs by individual agents with the goal of biasingcarpool plans to satisfy their preferences.

Designing the payment component of a dynamic and per-sonalized ridesharing system is a challenging problem. Asstated by the impossibility theorem, no exchange mechanismcan be efficient, budget balanced and individually rational[Myerson and Satterthwaite, 1981]. Moreover, computation-ally expensive payment calculations may not be feasible for adynamic system. In this work, we focus on VCG-based pay-ments as they promote truthful behavior and individual ratio-nality, and adapt to the changing preferences of users, in con-trast to simple payment methods such as basic cost sharing.

We shall present our initial VCG-based payment mechanism,and then explore the tradeoffs with applying the mechanismwithin the ABC prototype in terms of efficiency, computa-tional complexity, budget balance and individual rationality.

4.1 VCG Payments for ABCABC’s payment mechanism distributes VCG-based paymentsto promote truthful behavior, to ensure fairness and the ulti-mate sustainability of the system, while maximizing cumula-tive value of the collaboration [Vickrey, 1961; Groves, 1973;Clarke, 1971]. ρi, agent pi’s VCG payment to the system, iscalculated as below, given that V ∗

−i is the collaborative valueof the collection of rideshare plans SC∗ to all agents exceptpi, (V−i)∗ is the value of the collection of rideshare plansgenerated when pi is excluded from the ABC system:

ρi = (V−i)∗ − V ∗−i

If the rideshare policy calculated by the optimization com-ponent is optimal, the VCG payment mechanism is efficient–its output maximizes social value, is individual rational–allagents have positive utility by participating, and strategyproof–truth-telling is a dominant strategy.

The VCG payment component does not burden people byinquiring about the utility of each potential rideshare assign-ment. Instead, valuations are generated by the system basedon acquired preferences.

4.2 Tradeoffs on VCG Based PaymentsPursuing the use of VCG payments to ridesharing optimiza-tion immediately faces several challenges. First, the VCGpayment mechanism is not budget balanced, and may returna loss. Secondly, calculating VCG payments in a dynamicmechanism is computationally expensive. Third, VCG mech-anisms require the computation of optimal outcomes to en-sure truthfulness. The ABC system calculates VCG-basedpayments based on an approximate optimization of rideshareassignments and routes. Thus, agents are not necessarily in-cented to be truthful [Nisan and Ronen, 2007].

We modify the VCG payment scheme to adapt it to the dy-namic requirements of the open-world ridesharing problem.To simplify the analysis, we make the assumption that re-moving one agent from a carpool group does not affect therideshare allocation of agents outside of that group. We cal-culate local VCG-based payments, which computes the VCGpayment of agent pi only among the agents that share thesame carpool as pi. This assumption makes payment calcu-lations significantly more efficient, as carpool optimizationsfor payment calculations are done over a small subset of allagents. Calculating VCG payment locally offers an alter-native for efficient calculation of VCG-based payments, bypointing out an important tradeoff for implementing expen-sive payments efficiently. However, the assumption we maketo calculate VCG payments locally is not fundamental, doesnot affect the collaborative rideshare plans, and can be ig-nored if sufficient computational power is provided to com-pute payments globally.

We tested the local VCG-based payment scheme on a largedataset of GPS trails that we describe in more detail in Sec-tion 5. The experimental results show that value distribution

with local payments maintains 99.7% to 100% of individual-rationality among agents with varying fuel and time costs.However, the evaluation highlights the prospect of incurringa deficit with VCG-based payments. In our study, we foundthat the system pays drivers more than it collects from the pas-sengers. To sustain the carpooling system with local VCG-based payments, the system needs to distribute 55% to 79% ofthe cumulative value generated with carpools back to agentsas payments. The deficit of the system grows proportional tothe average time costs of the agents, as it gets harder to bringself-interested agents together when time cost is high.

Given the challenge with balancing the budget, we experi-mented with an alternate VCG-centric scheme, based on pre-vious work proposing a threshold-based mechanism that en-forces budget-balance as a hard constraint on payment calcu-lation [Parkes et al., 2001]. We modify the local VCG-basedpayment scheme with the threshold rule specified by Parkes,et al. to eliminate deficit where V ∗ is the cumulative value ofrideshare plans. ∆vick,i represents the non-negative portionof VCG payments which is called Vickery discount.

∆vick,i = V ∗ − (V−i)∗

For some parameter C ≥ 0, we define threshold discounts∆t

vick,i, and redefine payments ρti based on ∆t

vick,i. Thethreshold parameter C is calculated with linear programmingbased on local VCG-based payments and ∆vick,i values.

∆tvick,i = max(0, ∆vick,i − C)

ρti = vi(SC∗)−∆t

vick,i

Studies with the real-world commute dataset using the lo-cal VCG-based payments with the threshold rule demonstratethat the revised mechanism was able to eliminate the deficitfor a range of time and fuel cost values. The mechanism doesnot negatively influence the individual rationality nor the ef-ficiency of the ABC system.

With threshold-based payments and suboptimal outcomes,our mechanism is not guaranteed to be truthful. Investigat-ing the effect of using the local payments and threshold onthe truthfulness of agents will require a deeper analysis onthe system. Parkes et al., states that the threshold-based pay-ment scheme has better incentive properties than other rulesproposed in their work. Our threshold-based local VCG pay-ments promote truthful behavior as an agent’s payment doesnot directly depend on its preference revelation. We believethat the payment scheme is hard to manipulate by bounded-rational agents given the incomplete information available toagents about other agents and the indirect affect of an agent’spreferences on outcomes.

5 Real-World Trip Dataset and StudiesThe ABC prototype provides options for offline, batch op-timizations as well as for real-time simulations of incomingride requests based on the dynamic queuing of travel needsand preferences. Statistics are maintained on multiple dimen-sions of cost and savings for gaining insights into the opera-tion and sensitivity of the plan generation to different work-

loads and assumptions. The system also provides visualiza-tions of routes and route plans on a city map.

We ran studies based on the driving trip data gathered from215 subjects over a five-year period [Krumm and Horvitz,2005]. These subjects included Microsoft employees andspouses who volunteered to place GPS receivers with log-ging in their cars over several weeks in return for participat-ing in a random drawing for a prize. Nearly all the subjectslive in the Seattle, WA USA area. The GPS receivers wereprogrammed to record GPS data only when the users are inmotion. The dataset contains a total of 1,434,308 (latitude,longitude) points for an average of 6,671 points per partici-pant.

As the initial goal of this research is to generate carpoolplans for daily commutes of users, we segmented the datasetinto discrete trips. We identified any two consecutive GPSpoints that are either 5 minutes or more than 7 kilometersapart as two separate trips. The trips that are shorter thana threshold are eliminated, which resulted in 7,377 individ-ual trips. For each user, we selected a pair of morning andevening trips that appear to capture daily commute patternsof the users by having the following properties: (1) the regu-larity of the commutes on trip data of the user, (2) minimumdivergence of the selected commutes from a round trip. 215morning\evening commute patterns were extracted with anaverage duration of 26 mins for morning, 29 mins for evening,and average distance of 21km for morning and 24 km for theevening.

We tested the ABC prototype on commute patterns ex-tracted from the trip dataset. The results of the rideshare sys-tem are evaluated in terms of the efficiency on number of com-mutes (i.e., the reduction ratio on total number of commutes),efficiency on cost (i.e., the reduction ratio on total cost), andthe reduction on CO2 emissions. We explored the sensitiv-ity of the analyses to variations in the fuel costs (i.e., from$0.035/mile to $0.14/mile) and the average costs of time (i.e.,from $0/hour to $9.6/hour).

Figure 2: Seattle area map displaying the commute routes ofstudy participants (thicker blue lines represent more crowdedroutes) Left: Morning trips without ABC system, Right:Morning trips with ABC system. The ridesharing system re-duces the number of cars in the traffic significantly.

Figure 2 compares the individual commute plans with thecollection of rideshare plans generated by the system. Thethinner blue color on main highways indicates the positiveeffect of ridesharing on the morning commute traffic in theSeattle region. When the fuel cost is set to $0.07/mile2, andaverage time cost is set to $4.8/hour, ABC system is able toachieve 41% efficiency on number of commutes, 14% effi-ciency on total cost of transportation which results in 84.16tons of CO2 reduction per year.

Figure 3: Effect of fuel cost on the efficiency of ABC system.Increasing fuel costs improves the efficiency of ridesharing.

To investigate the influence of the cost of fuel on the effi-ciency of the rideshare optimization, we tested ABC over arange of fuel costs. As shown in Figure 3, the efficiency ofthe carpooling system on both the number of commutes andthe total cost improves significantly with increases in the costof fuel. These results indicate that increasing fuel costs canprovide higher incentives for agents to collaborate, and weexpect the willingness of agents to carpool to grow as fuelcosts increase. The reduction on CO2 emissions increases25% as fuel costs increases from 0.035/mile to $0.14/mile.

Figure 4: Influence of the average time cost on the efficiencyof ABC planning. Increasing time costs decreases the effi-ciency of ridesharing.

We investigated the influence of changes in the cost of timeon the efficiency of the rideshare system by varying the aver-age time costs of users as shown in Figure 4. As the costs oftime increase, the efficiency of the optimization with regard

2$0.07/mile is stated to be the per mile cost of driving byhttp://www.commutesolutions.org/calc.htm.

to the number of commutes and total costs incurred drops sig-nificantly. The reduction on CO2 emissions decreases 29.6%.Increasing time costs reduces the incentive of agents to col-laborate in ridesharing.

Figure 5: Effect of the size of agent set on the efficiency ofABC planning. The efficiency of ridesharing improves withthe number of users in the system.

We sought to understand how the density of actors mightchange the behavior and overall savings generated by the sys-tem. To simulate the effect of increasing the number of agentsin the system, we populated commute patterns with randomlycreated artificial commute patterns. The synthetic commutingrequests are generated by pairing randomly selected start/endpoints from the trips dataset, with trip start times taken from aGaussian distribution representing the start times of the com-mute patterns in the data. As displayed in Figure 5, the ef-ficiency of the system grows as the logarithm of the numberof the agents in the system. With more agents, the system ismore likely to find better matches for the users. Thus, we canexpect that the performance of the ridesharing system willimprove with increasing numbers of users.

6 Summary and ConclusionsWe reviewed research on reasoning and optimization for gen-erating shared transportation plans in a real-world setting. Weexplored the problem as an agent collaboration challenge anddeveloped extensions to prior work on coordination amongmultiple agents and market-based incentives to solve keychallenges. We constructed a prototype and explored the per-formance of the system with a dataset of real-world trips col-lected over five years. Our studies included sensitivity anal-yses that enable us to explore the influence on the behaviorof the system of changing such variables as the costs of fueland number of participants. In ongoing work, we are investi-gating new applications of the mechanisms and ideas, includ-ing within and beyond the transportation domain. Within thetransportation domain, we are exploring the use of the meth-ods to inform such decisions as to where to locate park andride facilities and additional practical issues with the deploy-ment of a dynamic version of the system in a running onlineservice that serves an organization or a larger city region 3.

3More detailed presentation of the ideas investigated in this workand the ongoing work on dynamic optimization, park-and-ride cen-

Other directions include assessing psychosocial factors andinvestigating how including these considerations in the largerutility function influences the rideshare plans generated. Webelieve that the ideas presented on generating shared plans forself-interested agents extend to numerous real-life domainswhere individual preferences and goals must be consideredin the generation of valuable collaborations. We hope that thechallenges highlighted in our pursuit of methods for promot-ing collaboration in real-world settings will motivate furtherresearch. Turning to the domain, we believe that there areopportunities for analogous applications of learning, infer-ence, optimization, and market mechanisms to address dif-ficult challenges with the environment and economy.

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