Task (re)allocation is a key problem in multiagent systems. Several different contract types have been introduced to be used for task reallocation: original, cluster, swap, and multiagent contracts. Instead of only using one of these contract types, they can be interleaved in a sequence of contract types. This is a powerful way of constructing algorithms that find the best solution reachable in a bounded amount of time. The experiments in this paper study how to best sequence the different contract types. We show that the number of contracts performed using any one contract type does not necessarily decrease over time as one might expect. The reason is that contracts often play the role of enabling further contracts. The results also show that it is clearly profitable for the agents to mix contract types in the sequence. Sequences of different contract types reach a solution significantly closer to the global optimum and in a shorter amount of time than sequences with only one contract type. However, the best sequences consist only of two interleaved contract types: original and cluster contracts. This allows us to provide a clear prescription about protocols for anytime task reallocation.

The capability to reallocate items-e.g. tasks, securities, bandwidth slices, MW hours of electricity, and collectibles-is a key feature in automated negotiation. Especially when agents have preferences over combinations of items, this is highly nontrivial. Marginal cost based reallocation leads to an anytime algorithm where every agent's utility increases monotonically over time. Different contract types head toward different locally optimal task allocations, and contracts from a recently introduced comprehensive contract type, OCSM-contracts, head toward the global optimum. Reaching it can take an impractically long time, so it is important to trade off solution quality against negotiation time. To construct negotiation protocols that lead to the best achievable allocations in a bounded amount of time, we compared sequences of four contract types. Original, cluster, swap, and multiagent contracts. The experiments show that it is profitable to use multiple contract types in the sequence: significantly better solutions are reached, and faster, than if only one contract type is used. However, the best sequences only include original and cluster contracts. Swap and multiagent contracts lead to bad local optima quickly. Interestingly, the number of contracts using any given contract type does not always decrease over time: contracts play the role of enabling further contracts.

Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also drastically outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.

We provide experimental results for a task allocation problem where serf-interested, individually rational agents (re)contract tasks among themselves. TraditionaJ contract types allow only one task to be transferred between agents at a time (original contracts). In this paper the original and four other contract types are studied: cluster-, swap-, multiagent, and OCSMcontracts. The OCSM-contracts will reach the global optimum even if the agents are individually rational, but in large-scale problems the number of steps required can be prohibitively large, albeit finite. In such cases it is more important to find the best solution reachable in a bounded amount of time. To construct algorithms that achieve that we study different contract types evaluate their performance. This paper discusses tile quality of local optima reached by the different contract types, and how quickly they are reached. It is shown how environmental characteristics such as the number of agents and the number of tasks affect these results. This analysis is used as a basis for making prescriptions about which contract types agents should use in different environments. Out of original-, cluster-, swap-, and multiagent-contracts, either original-contracts (if the ratio agents to tasks is great) or cluster-contracts (if the same ratio is small) reach a local optimum with a higher social welfare than the others.

Coalition formation is one of the key problems in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. This paper focuses on (cid:12)nding a worst case bound on how good the optimal coalition structure is compared to the best coalition structure that a nonexhaus-tive search (cid:12)nds. We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algo-rithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also drastically outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.

In automated negotiation systems consisting of self-interested agents, contracts have traditionally been binding, i.e., impossible to breach. Such contracts do not allow the agents to act e ciently upon future events. A leveled commitment protocol allows the agents to decommit from contracts by paying a monetary penalty to the contracting partner. The e ciency of such protocols depends heavily on how the penalties are decided. In this paper, di erent leveled commitment protocols and their parameterizations are empirically compared to each other and to several full commitment protocols. In the di erent domains, the agents are of di erent types: self-interested or cooperative and they can perform di erent levels of lookahead. Many di erent aspects of contracting are studied, such as social welfare achieved, CPU-time usage, and amount of contracting and decommitting. If a global clock is used for increasing the decommitment penalties, in nite decommitment loops are prevented, while a local clock cannot guarantee this. Concerning solution quality, the leveled commitment protocols are signi cantly better than the full commitment protocols of the same type, but the di erences between the di erent leveled commitment protocols are minor. Surprisingly, self-interested myopic agents reach a higher social welfare quicker than cooperative myopic agents when decommitment penalties are low. In all of the domains studied, the best way to set the decommitment penalties was to choose low penalties, but once that were greater than zero. The CPU-usage can be reduced by choosing the right mechanism of increasing the penalties. There is a trade-o between solution quality and CPUtime usage: both decrease with higher penalties. There is also a trade-o in the search for contracts to decommit from. If the rst pro table decommitment combination was chosen not so much CPU-time used, but the solution quality was worse. If the most pro table combination was chosen, social welfare was higher, but more CPU-time was used.iv BRYTBARA KONTRAKTS PRESTANDA I AUTOMATISKA HANDELSSYSTEM: EN EMPIRISK STUDIE SAMMANFATTNING I system f or automatisk handel, i vilka egoistiska agenter forhandlar, har kontrakten vanligtvis varit bindande och inte mojliga att bryta. Det medf or dock att agenterna inte kan anpassa sig till for andringar i omv arlden, p a ett for alla e ektivt satt. Ett protokoll som medger att man kan bryta godk anda kontrakt ar det leveled commitment protocol dar agenterna endast betalar en avgift till de andra agenterna i kontraktet om en agent skulle vilja bryta det. Hur e ektiva dessa leveled commitment protocol ar beror till stor del p a hur avgifterna for att bryta kontrakten best ams och hur hoga avgifterna ar. I detta arbete har olika satt att best amma avgifterna jamf orts och era olika parameteriseringar har unders okts. Agenterna i systemen har varit av olika typer: egoistiska eller samarbetsvilliga och de har utvarderat framtida handelser olika mycket. M anga olika aspekter av handelssystemens prestanda har studerats. N agra ar: CPU-tidsanv andningen, hur m anga kontrakt som ingicks och br ots, hur hog summan av alla agenternas vinst var. Om tiden, p a vilken upprakningen av avgifterna baseras, mats med en global klocka kommer inga oandliga loopar av ing angna och brutna kontrakt att upptrada. Detta inte ar mojligt om en lokal klocka anv ands. Resultatet var mycket battre an om kontrakt som inte gick att bryta anv andes, men skillnaderna mellan de olika protokollen som medgav att kontrakten kunde brytas var inte s a stor. Forv anade  ar att egoistiska agenter n ar en hogre total vinst an agenter som samarbetar om avgifterna for att bryta kontrakt ar l aga. Forbrukningen av CPU-tid kan minskas genom valet av metod f or att hoja avgifterna, men a andra sidan blir d a kvaliteten p a resultatet samre. v ACKNOWLEDGMENTS This Master's Thesis is submitted in partial ful llment of the requirements for the degree of Master's of Science from the School of Engineering Physics in conjunction with the Department of Numerical and Computing Science (NADA) at the Royal Institute of Technology (KTH), Stockholm, Sweden. This research was conducted in the Department of Computer Science at Washington University in St. Louis (WUSTL), U.S.A. I would like to thank my supervisors, Assistant Professor Tuomas Sandholm (WUSTL) and Associate Professor Viggo Kann (KTH) for giving me the opportunity to work on this thesis, and for their encouragement and support. I am especially grateful for the stimulating and motivating discussions I have had with Dr. Sandholm while working on this project. I would also like to thank Elizabeth Peterson, Mats Erixson, Simon Berg, and Kerstin Frenckner for their help in setting up the rst Master's Thesis defense held via video conference at the Royal Institute of Technology. I would also like to thank my fellow graduate students in the Department of Computer Science at Washington Universtiy for all of the help they provided during the research for this thesis and the writing of this paper. I especially would like to thank Kate Larson, Amy Murphy, Je rey Sass, William Shapiro, and Iftikhar Waheed. Last but not least I thank my family in Sweden for their support. vi TABLE OF CONTENTS ABSTRACT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iv BRYTBARAKONTRAKTS PRESTANDA I AUTOMATISKA HANDELSSYSTEM: EN EMPIRISK STUDIE : : : : : : : : : : : : : : : : : : v ACKNOWLEDGMENTS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vi LIST OF TABLES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xi CHAPTERS

In automated negotiation systems consisting of self-interested agents, contracts have traditionally been binding, i.e., impossible to breach. Such contracts do not allow the agents to act efficiently upon future events. A leveled commitment protocol allows the agents to decommit from contracts by paying a monetary penalty to the contracting partner. The efficiency of such protocols depends heavily on how the penalties are decided. Different leveled commitment protocols and their parameterizations are empirically compared to each other and to several full commitment protocols. Many different aspects of contracting are studied, such as social welfare achieved, CPU-time usage, and amount of contracting and decommitting. If a global clock is used for increasing the decommitment penalties, infinite decommitment loops are prevented, while a local clock cannot guarantee this. Concerning solution quality, the leveled commitment protocols are significantly better than the full commitment protocols of the same type, but the differences between the different leveled commitment protocols are minor.