As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it satisfies. Our aim in this paper is twofold: (1) to establish correspondences between certain types of weighted formulas and well-known classes of utility functions (such as monotonic, concave or k-additive functions); and (2) to obtain results on the comparative succinctness of different types of weighted formulas for representing the same class of utility functions.

In both individual and collective decision making, the space of alternatives from which the agent (or the group of agents) has to choose often has a combinatorial (or multi-attribute) structure. We give an introduction to preference handling in combinatorial domains in the context of collective decision making, and show that the considerable body of work on preference representation and elicitation that AI researchers have been working on for several years is particularly relevant. After giving an overview of languages for compact representation of preferences, we discuss problems in voting in combinatorial domains, and then focus on multiagent resource allocation and fair division. These issues belong to a larger field, known as computational social choice, that brings together ideas from AI and social choice theory, to investigate mechanisms for collective decision making from a computational point of view. We conclude by briefly describing some of the other research topics studied in computational social choice.

Abstract. A major challenge in the field of Multi-Agent Systems (MAS) is to enable autonomous agents to allocate tasks and resources efficiently. This paper studies an extended approach to a problem we refer to as the Collective Iterative Allocation (CIA) problem. This problem involves a group of agents that progressively refine allocations of teams to tasks. This paper considers the case where the performance of a team is variable and non-deterministic. This requires that each agent is able to maintain and update its probabilistic models using observations of each team’s performance. A key result is that each agent needs the capacity to store only two or three observations of a team’s performance to find near optimal allocations, and a further increase of this capacity will reduce the number of reallocations significantly. 1

We introduce a distributed negotiation framework for multiagent resource allocation where interactions between agents are limited by a graph defining a negotiation topology. A group of agents may only contract a deal if that group is fully connected according to the negotiation topology. An important criterion for assessing the quality of an allocation of resources, in terms of fairness, is envy-freeness: an agent is said to envy another agent if it would prefer to swap places with that other agent. We analyse under what circumstances a sequence of deals respecting the negotiation topology may be expected to converge to a state where no agent envies any of the agents it is directly connected to. We also analyse the computational complexity of a related decision problem, namely the problem of checking whether a given negotiation state admits any deal that would both be beneficial to every agent involved and reduce envy in the agent society.

To my parents and Anya. ii ACKNOWLEDGEMENTS First and foremost, I owe a lot of gratitude to my advisor, Ed Durfee. Without his support, patience, academic guidance, and technical advice, this dissertation would not have been possible. I especially want to thank Ed for giving me the freedom to explore and supporting me when I got excited about problems, even at times when he didn’t quite share my enthusiasm. I truly believe Ed’s top work priority is the growth of his students, and for that I offer my deepest thanks! I’m very grateful to the members of my committee, Kang Shin, Satinder Singh, Demos Teneketsis, and Michael Wellman for their valuable advice and insightful comments on my work. Michael Wellman deserves special credit for doing a very thorough job reviewing my thesis. I’m very thankful to my teachers at the University of Michigan, especially professors Martha Pollack and Kevin Compton. The administrators of the Michigan AI Lab deserve many thanks for their help in navigating various financial and administrative jungles. The support of Kelly Cormier, Colleen Neilson, and Wendy Anderson was truly indispensable. My friends in the AI Lab contributed significantly to making my life there fun, productive, and sometimes both. Thanks to all of you, and especially Jeff C., Joel W.,

Abstract. In distributed approaches to multiagent resource allocation, the agents belonging to a society negotiate deals in small groups at a local level, driven only by their own rational interests. We can then observe and study the effects such negotiation has at the societal level, for instance in terms of the economic efficiency of the emerging allocations. Such effects may be studied either using theoretical tools or by means of simulation. In this paper, we present a new simulation platform that can be used to compare the effects of different negotiation policies and we report on initial experiments aimed at gaining a deeper understanding of the dynamics of distributed multiagent resource allocation. 1

In this paper we attempt to analyze the problem of centrally allocating tasks to selfinterested agents in environments characterized by high uncertainty. The analysis is based on equilibrium dynamics, taking into account the agents ’ short-term and long-term considerations. The model reflects a rich realism by allowing both tasks and agents to dynamically arrive in the environment. This is correlated with real life scenarios where agents take part in a continuous process while having only partial information concerning the different world states and other agents ’ capabilities. Based on the comprehensive analysis of the equilibrium we present innovative algorithms that significantly facilitate the extraction of the agents ’ strategies for any specific settings. The findings are illustrated computationally and compared with parallel mechanisms for allocating the tasks in a closed environment and in a centralized enforceable manner. 1.

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Superman: “I’m here to fight for truth, justice, and the

We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing optimal—social welfare maximizing (maxsum)—allocations under the fairness notion of envyfreeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we ask: how good are these allocations? In particular, we provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envyfree allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations. 1