Noncooperative game theory provides a normative framework for analyzing strategic interactions.

The aggregation of conflicting preferences is a central problem in multiagent systems. The key difficulty is that the agents may report their preferences insincerely. Mechanism design is the art of designing the rules of the game so that the agents are motivated to report their preferences truthfully and a (socially) desirable outcome is chosen. We propose an approach where a mechanism is automatically created for the preference aggregation setting at hand. This has several advantages, but the downside is that the mechanism design optimization problem needs to be solved anew each time. Focusing on settings where side payments are not possible, we show that the mechanism design problem is NP-complete for deterministic mechanisms. This holds both for dominant-strategy implementation and for Bayes-Nash implementation. We then show that if we allow randomized mechanisms, the mechanism design problem becomes tractable. In other words, the coordinator can tackle the computational complexity introduced by its uncertainty about the agents' preferences by making the agents face additional uncertainty. This comes at no loss, and in some cases at a gain, in the (social) objective.

We develop a normative theory of interaction---negotiation in particular---among self-interested computationally limited agents where computational actions are game theoretically treated as part of an agent's strategy. We focus on a 2-agent setting where each agent has an intractable individual problem, and there is a potential gain from pooling the problems, giving rise to an intractable joint problem. At any time, an agent can compute to improve its solution to its own problem, its opponent's problem, or the joint problem. At a deadline the agents then decide whether to implement the joint solution, and if so, how to divide its value (or cost). We present a fully normative model for controlling anytime algorithms where each agent has statistical performance profiles which are optimally conditioned on the problem instance as well as on the path of results of the algorithm run so far. Using this model, we introduce a solution concept, which we call deliberation equilibrium. It is the perfect Bayesian equilibrium of the game where deliberation actions are part of each agent's strategy. The equilibria differ based on whether the performance profiles are deterministic or stochastic, whether the deadline is known or not, and whether the proposer is known in advance or not. We present algorithms for finding the equilibria. Finally, we show that there exist instances of the deliberation--bargaining problem where no pure strategy equilibria exist and also instances where the unique equilibrium outcome is not Pareto efficient.

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NP-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster—especially in cases with structure. CABOB’s search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem—the run-time distribution does not have a heavy tail.

The revelation principle is a cornerstone tool in mechanism design. It states that one can restrict attention, without loss in the designer's objective, to mechanisms in which A) the agents report their types completely in a single step up front, and B) the agents are motivated to be truthful. We show that reasonable constraints on computation and communication can invalidate the revelation principle. Regarding A, we show that by moving to multi-step mechanisms, one can reduce exponential communication and computation to linear---thereby answering a recognized important open question in mechanism design. Regarding B, we criticize the focus on truthful mechanisms---a dogma that has, to our knowledge, never been criticized before. First, we study settings where the optimal truthful mechanism is -complete to execute for the center. In that setting we show that by moving to insincere mechanisms, one can shift the burden of having to solve the -complete problem from the center to one of the agents. Second, we study a new oracle model that captures the setting where utility values can be hard to compute even when all the pertinent information is available---a situation that occurs in many practical applications. In this model we show that by moving to insincere mechanisms, one can shift the burden of having to ask the oracle an exponential number of costly queries from the center to one of the agents. In both cases the insincere mechanism is equally good as the optimal truthful mechanism in the presence of unlimited computation. More interestingly, whereas being unable to carry out either difficult task would have hurt the center in achieving his objective in the truthful setting, if the agent is unable to carry out either difficult task, the value of the center's objec...

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An alternating offers bargaining model for computationally limited agents is presented. The gents compute to determine plans, but deadlines restrict them from determining an optimal solution. As the agents compute, they also negotiate over whether to perform a joint plan or whether to act independently and how, if implemented, the value of the joint plan would be divided. Their computing actions and bargaining actions are interrelated and both incorporated into each agent's strategy. We analyze the model for equilibrium strategies for agents under different conditions. It is shown that the equilibrium strategies for the alternating offers model where agents take turns making offers and counter-offers, even with its extremely large action space, are equivalent to those of a much simpler single shot, take--it--or--leave--it bargaining model. In particular, agents will compute and make no offers until the first agent's deadline.

We analyze the computational and communication complexity of combinatorial auctions from a new perspective: the degree of interdependency between the items for sale in the bidders ' preferences. Denoting by Gk the class of valuations displaying up to k-wise dependencies, we consider the hierarchy G1 G2 # # Gm , where m is the number of items for sale. We show that the minimum non-trivial degree of interdependency (2-wise dependency) is sufficient to render NP-hard the problem of computing the optimal allocation (but we also exhibit a restricted class of such valuations for which computing the optimal allocation is easy). On the other hand, bidders' preferences can be communicated efficiently (i.e., exchanging a polynomial amount of information) as long as the interdependencies between items are limited to sets of cardinality up to k, where k is an arbitrary constant. The amount of communication required to transmit the bidders' preferences becomes super-polynomial (under the assumption that only value queries are allowed) when interdependencies occur between sets of cardinality g(m), ##.

Mechanism design is the art of designing the rules of the game (aka. mechanism) so that a desirable outcome (according to a given objective) is reached despite the fact that each agent acts in his own selfinterest.

Combinatorial auctions, where agents can bid on bundles of items (resources, tasks, etc.), are desirable because the agents can express complementarity and substitutability among the items. However, expressing one's preferences can require bidding on all bundles. We evaluate an approach known as incremental preference elicitation [3] and show that as the number of items increases, the amount of information required to clear the auction is a vanishing fraction of the information collected in direct revelation mechanisms. Most of the elicitors also maintain the benefit as the number of agents increases. We prove that randomization helps, in that no deterministic elicitor is a universal revelation reducer. Finally, we present a new query type that allows agents to use anytime algorithms to give approximate answers that are refined only as needed.