Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences (Bredereck, Elkind, Igarashi, AAMAS'19): each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents’ preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem.

Lifting Preferences over Alternatives to Preferences over Sets of Alternatives: The Complexity of Recognizing Desirable Families of Sets

The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating properties the lifted order should have. Well-known impossibility results by Kannai and Peleg and by Barberà and Pattanaik tell us that some desirable axioms – namely dominance and (strict) independence – are not jointly satisfiable for any linear order on the objects if all non-empty sets of objects are to be ordered. On the other hand, if not all non-empty sets of objects are to be ordered, the axioms are jointly satisfiable for all linear orders on the objects for some families of sets. Such families are very important for applications as they allow for the use of lifted orders, for example, in combinatorial voting. In this paper, we determine the computational complexity of recognizing such families. We show that it is Π2p-complete to decide for a given family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for all linear orders on the objects if the lifted order needs to be total. Furthermore, we show that the problem remains coNP-complete if the lifted order can be incomplete. Additionally, we show that the complexity of these problem can increase exponentially if the family of sets is not given explicitly but via a succinct domain restriction.

Preferences for Flexibility and Randomization under Uncertainty

An uncertainty-averse agent prefers betting on an event whose probability is known, to betting on an event whose probability is unknown. Such an agent may randomize his choices to eliminate the effects of uncertainty. For what sort of preferences does a randomization eliminate the effects of uncertainty? To answer this question, we investigate an agent's preferences over sets of acts. We axiomatize a utility function, through which we can identify the agent's subjective belief that a randomization eliminates the effects of uncertainty. (JEL D11, D81)

COALITION FORMATION GAMES: A SURVEY

In this paper we give an overview of various methods used to study cooperation within a set of players. Besides the classical games with transferable utility and games without transferable utility, recently new models have been proposed: the coalition formation games. In these, each player has his own preferences over coalitions to which he could belong and the quality of a coalition structure is evaluated according to its stability. We review various definitions of stability and restrictions of preferences ensuring the existence of a partition stable with respect to a particular stability definition. Further, we stress the importance of preferences over sets of players derived from preferences over individuals and review the known algorithmic results for special types of preferences derived from the best and/or the worst player of a coalition.

STABILITY OF PARTITIONS UNDER $\mathcal{WB}$-PREFERENCES AND $\mathcal{BW}$-PREFERENCES

Let a set of players be given and suppose that players have strict preferences over other players. The preferences are then extended to preferences over sets using the best (worst) player of a set and the worst (best) player as a tie-breaker. For such set-preferences we study the structure and computational questions connected with the existence problem of stable partitions. In the end, we review the known results for stable partitions under various preferences and point out some open questions.

The MarCon algorithm: A systematic market approach to distributed constraint problems

MarCon (Market-based Constraints) applies market-based control to distributed constraint problems. It offers a new approach to distributing constraint problems that avoids challenges faced by current approaches in some problem domains, and it provides a systematic method for applying markets to a wide array of problems. Constraint agents interact with one another via the variable agents in which they have a common interest, using expressions of their preferences over sets of assignments. Each variable integrates this information from the constraints interested in it and provides feedback that enables the constraints to shrink their sets of assignments until they converge on a solution. MarCon originated in a system for supporting human product designers, and its mechanisms are particularly useful for applications integrating human and machine intelligence to explore implicit constraints. MarCon has been tested in the domain of mechanical design, in which its set-narrowing process is particularly useful.