■ In (automated) negotiation systems for self-inter-ested agents, contracts have traditionally beenbinding. They do not accommodate future events.Contingency contracts address this but are oftenimpractical. As an alternative, we propose leveled-commitment contracts. The level of commitmentis set by decommitting penalties. To be freed fromthe contract, an agent simply pays its penalty tothe other contract party(ies). A self-interestedagent will be ruluctant to decommit because someother contract party might decommit, in whichcase the former agent gets freed from the contract,does not incur a penalty, and collects a penaltyfrom the other party. We show that despite suchstrategic decommitting, leveled commitmentincreases the expected payoffs of all contract par-ties and can enable deals that are impossible underfull commitment. Different decommitting mecha-nisms are introduced and compared. Practical pre-scriptions for market designers are presented. Acontract optimizer, ECOMMITTER, is provided on theweb.

The importance of automated negotiationsystems consisting of self-interestedagents is increasing. One reason is the

technology push of a growing standardizedcommunication infrastructure—the internet,the World Wide Web, EDI, HTML, KQML, FIPA, XML,JAVA, ODYSSEY, VOYAGER, CONCORDIA, AGLETS, and soon—over which separately designed agentsbelonging to different organizations can inter-act in an open environment in real time andsafely carry out transactions (Sandholm andFerrandon 2000). The second reason is strongapplication pull for computer support for con-tracting, especially at the operative decision-making level. For example, we are witnessingthe advent of small transaction business-to-consumer and consumer-to-consumer com-merce on the internet for purchasing goods,

services, information, communication band-width, and so on. Numerous electronic busi-ness-to business trading sites have alsoemerged, some of which already incorporateautomated negotiation capability. There is alsoan industrial trend toward virtual enterprises:dynamic alliances of small, agile enterprisesthat together can take advantage of economiesof scale when available (for example, by beingable to respond to larger and more diverseorders than they could individually) but donot suffer from diseconomies of scale.

Multiagent technology facilitates the auto-mated formation of such dynamic alliances onan order-by-order basis by automated contract-ing. Such automation can save labor time ofhuman negotiators, but in addition, other sav-ings are possible because computational agentsare often more effective at finding beneficialcontracts and contract combinations thanhumans are in strategically and combinatorial-ly complex settings. In traditional automatednegotiation mechanisms for self-interestedagents, once a contract is made, it is binding(see, for example Andersson and Sandholm[1999]; Cheng and Wellman [1998]; Kraus[1993]; Monderer and Tennenholtz [1998];Rosenschein and Zlotkin [1994]; Sandholm[1993]; Shoham and Tennenholtz [2001]). Thecontract parties cannot back out no matterhow future events unravel. Although a con-tract might be profitable to an agent whenviewed ex ante, it need not be profitable whenviewed ex post. Similarly, a contract that isunprofitable ex ante can become profitable expost. Full-commitment contracts are unable tocapitalize on the gains that such future eventscan provide.

However, many multiagent systems consist-ing of cooperative agents incorporate some

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Leveled-Commit-ment ContractingA Backtracking Instrument for

Multiagent Systems

Tuomas Sandholm and Victor Lesser

Copyright © 2002, American Association for Artificial Intelligence. All rights reserved. 0738-4602-2002 / $2.00

their fallback positions, but there is a contin-gency contract that both agents prefer overtheir fallbacks.

There are at least three major problems inusing contingency contracts among self-inter-ested agents, especially in automated negotia-tion.

First, the real-world party that an agent rep-resents often does not know all possible futureevents and cannot therefore use contingencycontracts optimally. Furthermore, even if thereal-world party does know them, program-ming this knowledge into an automated agentcan be prohibitively laborious or error prone.

Second, although contingency contracts canbe useful in anticipating a small number of keyevents, they become cumbersome as the num-ber of relevant future events to monitorincreases. In the extreme, all domain events(new tasks arriving, resources breaking downand becoming back online, and so on) and allnegotiation events (offers, acceptances, rejec-tions, and so on, from related negotiations)can affect the value of the original contract tothe agent and should therefore be conditionedon. Furthermore, these future events might notaffect the value of the original contract inde-pendently. The value of the original contractmight depend on combinations of the futureevents (Rosenschein and Zlotkin 1994; Sand-holm 1993; Sandholm and Lesser 1995). Thus,there is a potential combinatorial explosion ofpossible future worlds, and each of them mightneed to be associated with a different contin-gency, leading to a potential combinatorialexplosion of the contract (for example, the sizeof the contingency table that represents thecontract).

In addition to these two practical difficultiesassociated with contingency contracts, there isa third, fundamental problem. An event mightbe observable by only one of the contract par-ties. That agent might lie to the other partyabout the event in case the event is associatedwith a disadvantageous contingency to theobserving party. Thus, to be viable, contin-gency contracts would require an event verifi-cation mechanism that is not manipulable andnot prohibitively complicated or costly.

Leveled-Commitment ContractsTo avoid the drawbacks of contingency con-tracts, we propose another instrument for capi-talizing on the possibilities provided by proba-bilistically known future events. Instead ofconditioning the contract on future events, amechanism is built into the contract that allowsunilateral decommitting. This is achieved byspecifying in the contract decommitting penal-

form of decommitting possibility to allow theagents to accommodate new events. For exam-ple, in the original contract net protocol(Smith 1980), the agent that had contractedout a task could send a termination message tocancel the contract even when the contracteehad already partially fulfilled the contract. Thiswas viable because the agents were not self-interested: the contractee did not mind losingpart of its effort without compensation. Simi-larly, decommitting in automated contractingamong cooperative agents has been studied ina meeting scheduling domain (Sen and Durfee1998, 1994).

Unlike systems with cooperative agents,multiagent systems consisting of self-interest-ed agents require that we consider agents thatdo not follow externally specified strategies butchoose their own strategies. Therefore, theinteraction mechanism (that is, rules of thegame) has to be designed from the perspectiveof noncooperative game theory. Specifically,the mechanism should be designed so that (1)it is possible to determine what each agent’sbest strategy is from a self-interested, expectedutility-maximizing perspective (this can de-pend on the other agents’ strategies as wedemonstrate in this article) and (2) a desirablesocial outcome will follow even though everyagent uses its self-interested strategy.

One can think of negotiation as search amongmultiple agents where the search focus is theset of commitments made by the agents.Decommitting can then be viewed as backtrack-ing in this multiagent search. Although back-tracking has been used in multiagent systemsamong cooperative agents, for example, in dis-tributed constraint satisfaction (Yokoo 2000),the self-interest of agents imposes additionalrequirements on a backtracking instrumentbecause the system designer cannot control thecommitting and decommitting behavior of theagents. In this article, we discuss backtrackinginstruments that have desirable propertieseven when used among self-interested agents.

Contingency ContractsSome research in game theory has focused onusing the potential provided by probabilistical-ly known future events by contingency con-tracts among self-interested agents (Raiffa1982). The obligations of the contract are madecontingent on future events. There are gamesin which this mechanism provides an expectedpayoff increase to both parties of the contractcompared to any full-commitment contract.Also, some deals are enabled by contingencycontracts in the sense that there is no full-com-mitment contract that both agents prefer over

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ties, one for each agent. If an agent wants todecommit—that is, to be freed from the obliga-tions of the contract—it can do so simply bypaying the decommitting penalty to the otherparty. We call such contracts leveled-commitmentcontracts because the decommitting penaltiescan be used to choose a level of commitment.

The method requires no explicit condition-ing on future events: Each agent can do itsown conditioning. Therefore, no event-verifi-cation mechanism is required. Another poten-tial advantage is that the agents are not forcedto consider all combinations of possible futureevents up front, but rather, each agent canreact to only those events that actually occur.

Principles for assessing breach penalties havebeen studied in the economics of law (Calamariand Perillo 1977; Posner 1977), but the purposehas usually been to assess a penalty on the agentthat has breached the contract after the breachhas occurred. Similarly, penalty clauses for par-tial failure—such as not meeting a deadline—arecommonly used in contracts, but the purpose isusually to motivate the agents to abide by thecontract. Instead, in leveled-commitment con-tracts, explicitly allowing decommitting fromthe contract for a predetermined price is used asan active method for using the potential provid-ed by an uncertain future.1 As we discuss later, itturns out that, somewhat unintuitively, thedecommitting possibility can increase theexpected payoff for both contract parties.

Practical Motivations for Leveled CommitmentThe goal of the leveled-commitment contract-ing mechanism is to allow some flexibility, asin the case with no commitment while agentsare guaranteed some level of security, as in thecase of full commitment. Full-commitmentcontracts can be viewed as one end of a spec-trum with commitment-free contracts at theother. Leveled-commitment contracts spanthis entire spectrum based on how the decom-mitting penalties are chosen.2

There are several practical reasons why lev-eled commitment is desirable:

It allows agents to profitably accommodatenew domain events such as new tasks arrivingor resources breaking down by allowing anagent to back out of its old contracts that thesenew events have made unbeneficial or eveninfeasible.

It allows agents to profitably accommodatenew negotiation events such as new offers oroffer-acceptance messages. If these eventsmake some old contracts unbeneficial or infea-sible for an agent, the agent can decommitfrom those old contracts.

It provides a backtracking instrument fordistributed search (in the AI sense) that worksamong self-interested agents, unlike traditionalbacktracking techniques for distributed search(see Yokoo [2000] for a review of the traditionaltechniques). It allows more controlled prof-itable risk taking; thus, in terms of search, alow-commitment search focus is movedaround in the global search space of commit-ments (because decommitting is not unreason-ably expensive) so that more of the space canbe explored among self-interested agents thatwould otherwise avoid risky commitments. Forexample, in multiagent task allocation, anagent can accept a task set and later try to sub-contract out the tasks in this set separately.With full commitment, an agent would needto have standing offers from the agents it willsubcontract the tasks to, or it has to be able tohandle them (profitably) itself. With leveledcommitment, the agent can accept the task seteven if it is not sure about its chances of gettingthe tasks handled. If it does not get them han-dled, it can decommit.

It allows profitable construction of combina-torial contracts from basic contracts. Often, thevalue of a contract to an agent depends onwhich other contracts the agent will get(Rosenschein and Zlotkin 1994; Sandholm1993). Using leveled commitment, an agentcan take on unbeneficial contracts in anticipa-tion of later synergic contracts that will makethe sequence beneficial overall. If the later con-tracts in the sequence do not occur, the agentcan backtrack out of the first part of thesequence.

This method of constructing a combinatori-al contract through a sequence of basic con-tracts also applies to cases where the combina-torial contracts involve more than two parties.Contracts involving more than two parties areimportant for avoiding local optima in auto-mated negotiation: Even if no contract amongk agents is beneficial, a contract among k + 1agents can be (Andersson and Sandholm 2000,1999; Sandholm 1998).

It saves computation and time. In manyautomated negotiation applications, comput-ing the value of taking on a contract isintractable, so the agents have to resort toapproximation (Sandholm 1996, 1993; Sand-holm and Lesser 1995). Leveled commitmentallows an agent to bid based on a rough-valuecalculation. If the agent wins the bid, the agentcan invest a more thorough value calculation.If the contract no longer looks beneficial inlight of this more refined calculation, the agentcan decommit. The fact that only the winningbidders carry out a refined calculation can save

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Later in this article, we substantiate theadvantages of leveled-commitment contractsmore rigorously. However, before that, we dis-cuss some reasons why it is not obvious thatleveled commitment is advantageous.

Why Are the Advantages of LeveledCommitment Not Obvious?Despite the intuitive appeal and the practicalmotivations for leveled commitment, there areseveral reasons why it is not obvious that lev-eled-commitment contracts are superior tofull-commitment contracts.

First, when an agent decommits, its profitfrom decommitting can be smaller than theloss to the victim of the breach; both are com-puted after the decommitting penalties havebeen paid. Therefore, decommitting some-times decreases the sum of the contract parties’payoffs when viewed ex post.

Second, one might think that full-commit-ment contracts can never have a higher sum ofexpected payoffs to the contract parties thanleveled-commitment contracts because the lat-ter incorporate new information (new events),and according to decision theory, the expectedvalue of information is always nonnegative.However, this result from single-agent decisiontheory does not carry over to games wheremore than one party can receive new informa-tion. In such multiagent systems, informationcan have negative expected value. A twist onthe prisoners’ dilemma provides a simpleexample. Say that there are two players in sep-arate rooms, and each one can press one of twobuttons: (1) cooperate or (2) defect. Based onwhat buttons the agents press, they receivepayoffs according to table 1. Each agent’s dom-inant strategy is to defect, so the sum of theagents’ payoffs will be 1 + 1 = 2. Now, let usremove some of the information, namely, thelabels of the buttons. The agents will have topress at random, so the expected sum of pay-offs is 1/4(3 + 3) = 1/4(0 + 5) + 1/4(5 + 0) + 1/4(1+ 1) = 4.5; so, the expected value of the infor-mation is 2 – 4.5 = –2.5 < 0. Therefore, it is notobvious that leveled-commitment contracts—which incorporate more information—have ahigher (or even equal) sum of expected payoffsto the contract parties than full-commitmentcontracts.

Third, agents might decommit strategically.Consider a contractor agent that can awardone contract and a contractee agent that cantake on one contract. A nonstrategic agentwould decommit whenever its best outsideoffer, plus the decommitting penalty, is betterthan the current contract. However, a rationalself-interested agent would be more reluctant

computation systemwide. Also, the negotia-tions can be carried out faster because agentscan bid based on less computation.

It makes feasibility checks unnecessary.Before bidding with full commitment, anagent has to make sure that it can handle all itsobligations even if all its pending bids getaccepted. Such feasibility checks often use amajor portion of a contracting software agent’sdeliberation resources (Sandholm 1996, 1993).With leveled commitment, agents need notcarry out feasibility checks up front because ifan agent ends up overcommitted, it candecommit from some of the contracts to reob-tain feasibility. Avoiding feasibility checkssaves computation, and the negotiations canbe carried out faster because agents can bidbased on less computation.

It speeds up the negotiation process byincreasing parallelism. An agent can make(low-commitment) offers to multiple recipi-ents, although these offers are mutually exclu-sive from the agent’s perspective. In case morethan one recipient accepts, the agent can back-track from all but one, allowing the agent toaddress the recipients in parallel instead ofaddressing them one at a time and blocking towait for an answer before addressing the next.(Note that the alternative of sending an offerwith no commitment would be strategicallymeaningless).

It can be used to increase the contract par-ties’ welfare by reallocating risk. By choosingthe contract price and decommitting penaltiesappropriately, every agent’s expected utilitycan increase by making the less risk-averseagents carry more of the risk. The more risk-averse agents would be willing to compensatethe former agents with a higher expected pay-off. As we show, leveled commitment canincrease the contract parties’ expected payoffseven if the agents are risk neutral. The use ofthis instrument as a risk reallocation tool pro-vides an additional utility increase to the con-tract parties. For simplicity, we do not addressrisk reallocation in this article.

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Column Player Cooperate Defect

Row Cooperate 3, 3 0, 5Player Defect 5, 0 1, 1

Table 1. Prisoners’ Dilemma Game.In each square, the row player’s payoff is listed first.

in decommitting because there is a chancethat the other party will decommit, in whichcase, the former agent gets freed from the con-tract obligations, does not have to pay adecommitting penalty, and will collect adecommitting penalty from the other party.Similarly, the other contract party will bereluctant to decommit for the same reason.Because of such reluctant decommitting, acontract might end up being inefficiently kepteven though each party would be better offdecommitting and paying the penalty (andtherefore, the sum of the contract parties’ pay-offs would be higher if either agent alone, orboth agents, would decommit).

Next, we show that leveled-commitmentcontracts are superior to full-commitment con-tracts despite these concerns.

The GameThe benefits of leveled commitment can bedemonstrated already in a relatively simplecontracting setting with two risk-neutralagents, each of which attempts to maximize itsown expected payoff. We call one of the agentsthe contractor and the other agent thecontractee.

A full-commitment contract between thecontractor and the contractee is defined by thecontract obligations, which include (1) adescription of what each of the two agents hasto perform (handling tasks, contributinggoods, lending resources, and so on) and (2) acontract price that the contractor has to pay tothe contractee.

Say that the value (or cost) of executing thecontract description can change for eachagent separately. At contract time, each agentonly has probabilistic information about thisvalue. The change in value can stem fromchanges in the agent’s own characteristics,such as resources failing or becoming avail-able. The change can also be the result ofcomputation: Based on a rough computation,a contract’s value might have looked differentthan it looks after a more refined computa-tion. Furthermore, the value of a contract canchange because of changes in outside optionssuch as offers from third parties. Our frame-work and results are not specific to any partic-ular source of change. However, we presentour results in the setting where the changestems from outside options. Specifically, theagents might receive outside offers. For sim-plicity, say that all offers have the samedescription, so price is the only concern, andeach of the two agents only want to beinvolved in one contract (the contractor gets

its task handled and does not need to have ithandled more than once, and the contracteehas limited resources and can only take onone contract).

For the analysis, say that the contractor’sbest (lowest) outside offer is not known exante, but the probability distribution fromwhich it will be drawn is known. Similarly,the contractee’s best (highest) outside offer isunknown, but it will be drawn from anotherknown distribution. If an agent does notreceive an outside offer, its “best outsideoffer” corresponds to its best outstandingoutside offer or its fallback payoff. The advan-tages of leveled commitment prevail even ifthe outside offers are statistically indepen-dent, and the figures in this article depictsuch settings. For the analysis, the prior dis-tributions of outside offers are assumed to becommon knowledge between the contractorand the contractee. This assumption of com-monly known priors is arguably close to accu-rate in applications where the agents havegood statistical information on how much itcosts to have the contract description filled.For example, if one were to sell an airline tick-et using a leveled-commitment contract,there are good statistics about how much anairline can charge for a seat on a certain leg aswell as statistics on how much it costs a pas-senger to travel this leg using a choice of anyairline.

The contractor and the contractee caneither make a contract or wait for their out-side offers. If the contractor and the con-tractee do make a contract, they can choose touse some full-commitment contract or someleveled-commitment contract. A leveled-com-mitment contract between a contractor and acontractee is defined by four components: (1)a description of what each of the two agentshas to perform (handling tasks, contributinggoods, lending resources, and so on), (2) acontract price that the contractor has to payto the contractee, (3) the contractor’s decom-mitting penalty, and (4) the contractee’sdecommitting penalty.

If an agent decommits and pays its penalty,then the contract description does not needto be fulfilled, and the contract price does notneed to be paid. We say that each of the twoagents observes its own outside offers beforehaving to decide whether to decommit, butthe agents do not observe each other’s outsideoffers. This seems realistic from a practical(automated) contracting perspective.

An easy way to think about the outsideoffers is to consider them to be full-commit-ment contracts. Alternatively, they can be

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Decommitting Strategies under Different Leveled-

Commitment MechanismsThe equilibrium of the decommitting gamediffers significantly in different variants of lev-eled-commitment contracting mechanisms.We identified two natural dimensions alongwhich these mechanisms can differ.

Along one dimension, there are three differ-ent orders in which the agents have to revealtheir decommitting decisions: contractor first,contractee first, or simultaneously. The key dis-tinction is not whether decommitting happensat the same point in time but whether an agentknows the other agent’s decommitting deci-sion by the time it has to reveal its own decom-mitting decision. If neither agent knows theother’s decision at this stage, the decommittingis in essence simultaneous.5

Along the second dimension, there are twochoices of what happens if both agents decom-mit. Either both pay the penalties to each oth-er, or neither pays a penalty.

These dimensions set up a space of 3 x 2 = 6leveled-commitment contracting mechanisms.

In the sequential games, if the first agentdecommits, the second agent would neverdecommit because it could only reduce its pay-off by doing so. Therefore, in the sequentialgames (contractor first or contractee first), thevariant where both pay if both decommit isequivalent to the variant where neither pays ifboth decommit. Thus, four distinct mecha-nisms are left. Of these, the sequential mecha-nism where the contractor moves first and thesequential mechanism where the contracteemoves first are analogous, which leaves threefundamentally different mechanisms: (1)sequential decommitting (say, contractee first);(2) simultaneous decommitting, both pay if bothdecommit; and (3) simultaneous decommitting,neither pays if both decommit.

The equilibrium differs across these mecha-nisms. It is easy to observe that in the sequen-tial game, if the first agent does not decommit,then the second agent will decommit non-strategically (truthfully). However, the firstagent’s behavior is strategic and requires quan-titative analysis. In the simultaneous games,both agents’ strategies require quantitativeequilibrium analysis. We conducted theseanalyses (Sandholm 1996; Sandholm and Less-er 2001), and the results that we discuss in thisarticle are based on this work. These results aregeneral and apply to any distributions ofuncertainty. However, to keep the presentationnonmathematical in this article, we onlydemonstrate the equilibria of the games graph-

expected utilities that the agents get under out-side leveled-commitment contracts.

Our game consists of three stages. In the firststage, which we call the contracting game, theagents choose a contract (or no contract). Inthe second stage, each agent receives its out-side offers. In the third stage, which we call thedecommitting game, the agents decide onwhether to decommit or not. Clearly, how theagents will play in the decommitting gameaffects their preferences over contracts in thecontracting game. We say that a contract isindividually rational for an agent if the agent’sexpected payoff under the contract is higherthan this agent’s expected payoff would be ifthe agent made no contract and waited for itsbest outside offer. A contract is called individ-ually rational if it is individually rational forboth agents.

A nonstrategic (truthful) agent woulddecommit whenever its outside offer is betterthan the existing contract plus its decommit-ting penalty. However, we do not assume thatthe agents decommit nonstrategically. In-stead, a self-interested agent can decommitstrategically. It might be more reluctant todecommit than a nonstrategic agent would bebecause there is a chance that the other con-tract party will decommit; in which case, theagent gets freed from the contract obligations,does not have to pay a penalty, and will col-lect a penalty from the other agent. At thesame time, the other agent will be reluctant todecommit as well.

Each agent’s decommitting strategy is char-acterized by the agent’s decommitting thresh-old. If the contractor’s outside offer is lowerthan the contractor’s threshold, then the con-tractor will decommit. Similarly, if the con-tractee’s outside offer is greater than the con-tractee’s threshold, then the contractee willdecommit.

To analyze such situations, one needs todetermine which strategy would be best for aself-interested agent, and only then can oneexpect a self-interested agent to use this strat-egy. The interesting aspect of the decommit-ting game is that neither agent has a dominantstrategy. How an agent should set its decom-mitting threshold depends on how the otheragent sets its threshold. Therefore, we analyz-ed the (Nash) equilibrium of the decommit-ting game where the contractor’s threshold isa best response to the contractee’s, and thecontractee’s threshold is a best response to thecontractor’s. If others design their softwareagents to act in this manner, then no agentdesigner can do better than designing his/heragent to act this way.

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ically in the context of a particular example. Consider a contracting setting where the

contractor’s best (lowest) outside offer is drawnfrom a uniform distribution on [0, 100], andthe contractee’s best (highest) outside offer isdrawn from a uniform distribution on [0, 110].Figure 1 illustrates the equilibria for the threedifferent leveled-commitment mechanisms. Toavoid drawing in three dimensions, we fixedthe value of the contract price (to 52.5, whichis halfway between the contractor’s expectedbest outside offer [50] and the contractee’sexpected best outside offer [55]).

Figure 1 shows the Nash equilibrium decom-mitting thresholds of our example. As we movefrom the left graphs to the right graphs, weincrease the contractor’s penalty. Within eachgraph, we vary the contractor’s penalty b, andthe equilibrium moves in the plane according-ly. In each graph, a point (x, y) corresponds toan equilibrium; that is, the contractor decom-mits if its outside offer is lower than x, and the

contractee decommits if its outside offerexceeds y. (However, in the sequential game,the contractor never decommits if the con-tractee decommits.) In each graph, the Nashequilibrium deviates from nonstrategic(“truthful”) decommitting. In cases where theequilibrium point is outside the frame (that is,outside the support of the distribution of theagent’s best outside offer), it is sure that thecorresponding agent will not decommit.

Figure 1 shows that in the simultaneousgame where both pay the penalties if bothdecommit, as an agent’s penalty approacheszero, the agent becomes truthful, but the oppo-nent does not. On the contrary, in the simulta-neous game where neither pays if both decom-mit, as an agent’s penalty approaches zero, theagent does not become truthful, but the oppo-nent does! We showed that these phenomenaprevail, in fact, under any distributions of out-side offers, not only in this example (Sand-holm and Lesser 2001).

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Figure 1. The Nash Equilibrium Decommitting Thresholds of Our Example.

any full-commitment contract. Furthermore, itturns out that each one of the leveled-commit-ment mechanisms can be used to strictlyincrease the expected payoffs of both contractparties. It follows that there are games (definedby the distributions of outside offers) where nofull-commitment contract is possible (becauseat least one agent would rather just wait for itsbest outside offer), but a leveled-commitmentcontract is possible because each contract partyprefers it over waiting for the best outside offer.In other words, leveled commitment enablesdeals, which can be shown even in the simpleexample earlier where the contractor’s best out-side offer is uniformly distributed on [0,100]and the contractee’s on [0,110]. The contractorwould accept a full-commitment contract ifthe price were below 50. The contractee wouldaccept a full-commitment contract if the pricewere above 55; so, there is no mutually accept-able full-commitment contract in this exam-ple. However, we can construct a leveled-com-mitment contract that works. We proved thisanalytically (Sandholm 1996; Sandholm andLesser 2001]; here, we simply illustrate the finalresults. Figure 2 shows the leveled-commit-ment contracts that are individually rational inthis game where no full-commitment contractis. The figure shows them for the simultaneousdecommitting game where neither pays apenalty if both decommit. The figures for theother decommitting mechanisms are similarbut not identical.

Another general fact is the relative amountof strategy that the mechanisms induce. Let pin the simultaneous mechanisms be the prob-ability that the opponent decommits or, in thesequential mechanism, the probability that thesecond mover decommits given that the firstmover did not decommit. Now, for given p,given contract price, and given decommittingpenalties, the (first) agent is most strategic(reluctant to decommit) in the sequentialmechanism, less strategic in the simultaneousmechanism where both pay if both decommit,and least strategic in the simultaneous mecha-nism where neither pays if both decommit(Sandholm and Lesser 2001).

Beyond these general principles, Sandholmet al. designed and built a system, ECOMMITTER,3

which—given the contract price, decommit-ting penalties, and distributions of outsideoffers—finds the equilibrium decommittingthresholds for each of the six leveled-commit-ment mechanisms (Sandholm, Sikka, and Nor-den 1999).

Leveled Commitment Increasesthe Contract Parties’ Payoffs and

Enables Deals Because a leveled-commitment contract canemulate full commitment by setting the penal-ties high enough, there always exists a leveled-commitment contract that is at least as good as

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Contracteewill surelynot decommit

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Contractor'sdecommittingpenalty

Figure 2. The Gray Regions Correspond to Three Qualitatively Different Classes of Leveled-Commitment Contracts That Both Parties Prefer over Waiting for Their Outside Offers.

To avoid drawing in three dimensions, we fix the contract price to a particular value (52.5). Other choices workas well: The set of individually rational contracts forms a three-dimensional volume.

In addition to enabling deals thatare impossible using full-commitmentcontracts, leveled-commitment con-tracts can increase the economic effi-ciency of a deal even if a full-commit-ment contract were possible. Thereverse cannot occur because leveled-commitment contracts can emulatefull-commitment contracts by settingthe penalties high enough. We quanti-tatively characterized the uncertaintythat leveled-commitment contractscan profitably capitalize on and uncov-ered the following simple rule: Leveledcommitment increases the contractparties’ payoffs if there is some chancethat the contractor’s outside offer islower than the contractee’s expectedoutside offer or some chance that thecontractee’s outside offer is higherthan the contractor’s expected outsideoffer (Sandholm 1996; Sandholm andLesser 2001). Note that this conditioncan be satisfied even if only one agent’sfuture involves uncertainty.

Optimizing the ContractParameters and Dividing

the SurplusUsually there is either no contract thatis individually rational for the agents(better for both than waiting for out-side offers), or there are many suchcontracts. Bargaining theory addressesthe choice among individually ratio-nal deals, usually by modeling timediscounting (Kraus, Wilkenfeld, andZlotkin 1995; Rubinstein 1982), dead-lines (Sandholm and Vulkan 1999), orbargaining costs (Rubinstein 1982) inthe bargaining process or by assertingdesirable properties that the chosencontract should have [Nash 1950;Osborne and Rubinstein 1990]. In thisarticle, we do not address the choiceamong individually rational contracts.Algorithms for determining the indi-vidually rational contracts (contractprice and decommitting penalties)that maximize the sum of the contractparties’ payoffs are presented in Sand-holm et al. (1999).4

One conceivable concern is that thissurplus might only be maximizedunder certain splits of the surplusbetween the contract parties. However,it was recently shown that for any ofthe six leveled-commitment mecha-

nisms, the surplus can be maximizedunder any split of the surplus byappropriately setting the contract priceand decommitting penalties (Sand-holm and Zhou 2000). This makes theleveled-commitment contract technol-ogy a modular component for (auto-mated) negotiation. It can be used as atool for increasing surplus in settingswith uncertainty and using any (bar-gaining) mechanism for deciding howto divide the surplus between the con-tract parties.

Another concern is what happens ifa contract party misperceives the distri-butions of outside offers. We showedthat in settings where only one agent’soutside offers are uncertain, a misper-ceiving agent can only hurt itself, butin games where more than one agent’soutside offers are uncertain, a misper-ceiving agent can also hurt the othercontract party by bad decommittingdecisions (Sandholm and Lesser 2001).

Which Leveled-Commit-ment Mechanism Is Best?

As shown in figure 1, for any givencontract, the equilibria are differentfor the different decommitting mech-anisms. It turns out that the surplusmaximizing contract parameters alsodiffer across the mechanisms (Sand-holm, Sikka, and Norden 1999). How-ever, a recent paper shows that surpris-ingly, among risk-neutral agents, eachof the six mechanisms leads to thesame sum of the contract parties’ pay-offs when the contract price andpenalties are optimized for each mech-anism separately (Sandholm and Zhou2000). (Among agents that are not riskneutral, the three mechanisms lead todifferent sums of utilities, and theranking of the mechanisms variesbased on the agents’ utility functions.)

Because the sum of the contract par-ties’ payoffs cannot be used as the cri-terion for choosing a mechanismamong risk-neutral agents, other crite-ria are needed.

One practical goal is to minimize thenumber of payment transfers. A recentpaper shows that if the contract is opti-mized separately for each of the mech-anisms, among risk-neutral agents, theoptimal decommitting thresholds willbe the same for all six mechanisms

(Sandholm and Zhou 2000). Therefore,the mechanisms can be comparedbased on what happens depending onwhere the outside offers fall withrespect to these thresholds. If oneagent gets an offer that is better thanits threshold but the other agent doesnot, all the mechanisms lead to onepenalty being paid. If neither agentreceives an offer that is better than itsthreshold, all the mechanisms lead tono penalty payments. If both agentsreceive offers that are better than thethresholds, both will decommit in thesimultaneous games, but only the firstagent will decommit in the sequentialgame. In this case, the simultaneousmechanism where both pay leads totwo payments, the sequential mecha-nism leads to one, and the simultane-ous mechanism where neither paysleads to none. In summary, from theperspective of minimizing the numberof penalty payments, the simultaneousmechanism where neither pays if bothdecommit is best, the sequential mech-anism is in the middle, and the simul-taneous mechanism where both pay ifboth decommit is worst.

Another evaluation criterion is ro-bustness of the equilibrium in thedecommitting game. For the sequen-tial decommitting game, we were ableto use iterated dominance as the solu-tion concept, but for the simultaneousdecommitting games, the Nash equi-librium was used. This suggests usingsequential decommitting mechanismsbecause iterated dominance is a morerobust solution concept than the Nashequilibrium (Mas-Colell, Whinston,and Green 1995).

An additional consideration thatfavors sequential decommitting mech-anisms is that playing optimally iseasy for one of the agents (the secondmover). The second mover is best offby decommitting nonstrategically ifthe first mover did not decommit andnot at all if the first mover did.

Finally, a recent article shows thatthe equilibrium is always unique inthe sequential mechanisms, but mul-tiple equilibria can exist in the simul-taneous mechanisms (Sandholm, Sik-ka, and Norden 1999). This alsospeaks in favor of using the sequentialmechanisms.

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signs that allow bidding on bundles,one can obtain efficient outcomes indominant strategy equilibrium (see,for example, Sandholm [2000]). How-ever, this can require a bidder to com-pute its valuation for each combina-tion of items and to bid for eachcombination. Also, the auctioneer’stask of determining the winners iscomputationally complex (Sandholm2002). A potentially more practicalalternative is to use sequential orascending auctions with bidding onindividual items or restricted combi-nations only. Leveled-commitmentcontracts could be used as a mecha-nism for bidders to put back items ifthey do not (or if they project thatthey will not) obtain the combina-tions that they want. Similarly, theauctioneer might want to exercise atake-back, for example, if it receives abetter bid later. Different one-sided,put-back mechanisms have alreadybeen tried in auction contexts (McAfeeand McMillan 1996; Walsh and Well-man 1999), but leveled-commitmentcontracts allow both put-backs andtake-backs. This gives rise to additionalphenomena—such as strategic decom-mitting. Leveled-commitment con-tracts can also prove useful in onlinebuying scenarios where a shoppingagent can buy an item from multiplealternative sites (auctions, catalogs,and so on), and the suppliers can selltheir goods to multiple alternativebuyers. If an agent (buyer or seller)then gets offered a better deal than theone it has obtained to this point, it candecommit.

Future ResearchThere are several interesting directionsfor future research on leveled-commit-ment contracts.

Even if explicit linking of issuesusing combinatorial contracts (withpotentially more than two agents percontract) is allowed, leveled-commit-ment contracts can be beneficial. Iden-tifying profitable combinatorial con-tracts can be complex computation-ally and difficult without a globalview, so an agent might be better offtrying to construct profitable combi-nations from sequences of individualcontracts, each with leveled commit-

in the negotiations, which can alsosave computation.

Interestingly, some element of glob-al clock is required as the basis forincreasing the penalties: To avoid infi-nite loops among myopic agents, itdoes not suffice to count time fromthe moment when each contract ismade (Andersson and Sandholm1998). There are also interesting issuesin how to increase the penalties to getenough backtracking to reach goodsolutions but not too much to wastetime. The results differ depending onwhether the agents are myopic(Andersson and Sandholm 1998) orcarry out strategic look ahead (Ander-sson and Sandholm 2001).

ConclusionsLeveled-commitment contracts arenew backtracking instruments formultiagent systems that work evenamong self-interested agents thatdecommit strategically. Leveled com-mitment can increase the payoffs of allcontract parties when at least one ofthe agents faces uncertainty. Thesecontracts are more practical than con-tingency contracts. However, theygenerally achieve a lesser sum of pay-offs than the optimal complete con-tingency contract (that uses event ver-ification) because sometimes thecontract will be kept although itshould be dissolved. The results andalgorithms that we discussed in thisarticle also extend to leveled-commit-ment contracts that involve morethan two contract parties in a singlecontract (Sandholm, Sikka, and Nor-den 1999).

Since we introduced leveled-com-mitment contracts (Sandholm andLesser 1995), they have been used inseveral applications. For example, Mit-subishi has applied them to an elec-tronic market for construction wasterecycling in Japan (Akiyoshi et al.1999). They have also been applied toautomated negotiation in a manufac-turing setting (Collins et al. 1998) andin a digital library (Park, Durfee, andBirmingham 1996).

Multiitem auctions where biddershave preferences over combinations ofitems are another important potentialapplication. With certain auction de-

Decommitting Cascades,Infinite Decommit-

Recommit Loops, andIncreasing Penalties

In a web of multiple contracts (poten-tially involving several agents each),full-commitment contracts induceone negotiation search focus consist-ing of the obligations of the contracts.With leveled-commitment contracts,there are multiple such foci, and anyagent involved in a contract canswitch from one such focus to anotherby decommitting from some contract.This decommitment can make it ben-eficial for another agent to decommitfrom another contract, and so on,leading to cascades of backtracks. Anappropriate amount of backtracking isdesirable in the search for good alloca-tions of obligations among the agents.

However, with myopic agents thatuse leveled-commitment contracts,the multiagent system can get stuck inan infinite loop of states (where eachstate is defined by the commitmentsthat the agents hold) (Andersson andSandholm 1998). The agents make asequence of deals and then backtrackout of them in nonchronologicalorder. Then the process repeats. Toavoid such useless loops of decommit-ting and recommitting, recommittingcould be disabled. The mechanismcould specify that if a contract offer isaccepted and later either agent decom-mits from the contract, the originaloffer becomes void as opposed to stay-ing valid according to its originaldeadline that might not have beenreached at the time of decommitment.However, even if agents cannot explic-itly recommit to a contract, it is hardto monitor that they will not makeanother identical deal, again givingrise to the possibility of the equivalentof useless decommit-recommit loops.Useless decommit-recommit loops canbe tackled using decommitting penal-ties that increase with time (real timeor number of domain events or nego-tiation events).6 This allows a low-commitment negotiation focus to bemoved in the joint search space andstill make the contracts meaningful bysome level of commitment. The in-creasing level of commitment causesthe agents to not backtrack too deeply

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ment. The best contracting mecha-nisms will most likely combine leveledcommitment and explicit linking ofissues. As a first step in this direction,hybrid negotiation mechanisms weredeveloped where leveled commitmentwas used on top of combinatorial con-tracts (Andersson and Sandholm1998). These contracts were studied insimulation.

Another open question is how anagent should allocate its scarce com-putational resources when evaluatingdifferent leveled-commitment con-tracts. Which combinations of dealsshould it evaluate? How much of theevaluation should it conduct beforebidding and how much after winning?Steps toward devising normative theo-ries of deliberation in other gameshave already been taken (Larson andSandholm 2001a, 2001b, 2001c; Sand-holm and Lesser 1997). These modelsare likely to help in addressing thedeliberation question in leveled-com-mitment contracting, but this workalso uncovered some complications.For example, it turned out that how anagent is best off deliberating dependson how others deliberate. Therefore, agame-theoretic equilibrium analysiswas conducted in the space of theagents’ deliberation strategies.

The deliberation capabilities of theagents should also be taken intoaccount when designing leveled-com-mitment mechanisms. For example,they are likely to affect the best pace ofincreasing the decommitting penal-ties, which opens up a whole newavenue in game-theoretic mechanismdesign.

AcknowledgmentsThis material is based on work sup-ported by the National Science Foun-dation under CAREER award IRI-9703122 and grants IIS-9800994, ITRIIS-0081246, and ITR IIS-0121678.

Notes1. Decommitting has been studied in othersettings, for example, where there is a con-stant inflow of agents, and they have a timecost for searching partners of two types:good or bad (Diamond and Maskin 1979).

2. Different parts of the contract could beassociated with different decommittingpenalties (Sandholm 1996; Sandholm andLesser 1995), which could be handled by

considering the parts as separate contracts.

3. www.cs.cmu.edu/ ˜amem/eMediator.

4. The contract optimization service, ECOM-MITTER, is available at www.cs.cmu.edu/˜amem/eMediator.5. An agent would have an incentive to tryto outwait the other and thus turn a simul-taneous mechanism into a sequentialmechanism where the opponent declaresits decommitting decision first. Such post-poning can be avoided by using a trustedthird party that does not announce thedecommitting decisions until it hasreceived the decisions from both parties.This can also be accomplished without athird party if each agent encrypts its deci-sion that it sends to the other and sends outthe key only after receiving the opponent’sencrypted decision.

6. The decommitting penalty could alsodecrease as a function of acceptance time ofthe offer or be conditioned on events inother negotiations or the environment.

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Tuomas Sandholm is anassociate professor in theComputer Science De-partment at CarnegieMellon University. Hereceived a Ph.D. and anM.S. in computer sciencefrom the University ofMassachusetts at Am-

herst in 1996 and 1994, respectively. Heearned an M.S. (B.S. included) with distinc-tion in industrial engineering and manage-ment science from the Helsinki Universityof Technology in 1991. While a researchscientist at the Technical Research Centerof Finland (1990–1992), he built the TRA-CONET system, one of the first distributedautomated negotiation systems for self-interested agents. From then on, hisresearch has focused on designing andbuilding multiagent systems, mainly forelectronic commerce, that handle bothself-interest and computational complexi-ty. Several of his systems have been com-mercially fielded. He has published over125 technical papers and received numer-ous academic awards, including the NSFCareer Award and the inaugural ACMSIGART Autonomous Agents ResearchAward. His e-mail address is sandholm@cs.cmu.edu.

Victor Lesser has been aprofessor of computerscience at the Universityof Massachusetts at Am-herst since 1977 andserves as the director ofthe Multi-Agent SystemsLaboratory. He receivedhis Ph.D. in computer

science from Stanford University in 1972and then was a research scientist atCarnegie-Mellon University, where he wasthe systems architect for the HEARSAY-II

speech understanding system, which wasthe first blackboard system developed. Hismajor research focus is on the control andorganization of complex AI systems. Lesseris a founding fellow of the American Asso-ciation for Artificial Intelligence. HIs e-mailaddress is lesser@cs.umass.edu.