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 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 analyze the perfect Bayesian equilibria of the games which 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. Finally, we present algorithms for finding the equilibria.
Coalition formation is a key topic in multiagent systems. One would prefer a coalition that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow for exhaustive search for the optimal one. We present experimental results for three anytime algorithms that search the space of coalition structures. We show that, in the average case, all three algorithms do much better than the recently established theoretical worst case results in Sandholm et al.(1999). We also show that no one algorithm is dominant. Each algorithm's performance is influenced by the particular instance distribution, with each algorithm outperforming the others for different instances. We present a possible explanation for the behavior of the algorithms and support our hypothesis with data collected from a controlled experimental run.
Coalition formation is a key topic in multiagent systems. One may 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. Furthermore, finding the optimal coalition structure is NP-complete. 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 significantly outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents.