A Formalization of Equilibria for Multiagent Planning

Traditionally, planning involves a single agent for which a planner needs to find a sequence of actions that can transform some initial state into some state where a given goal statement is satisfied. But in general, “planning” can be viewed as being concerned with a general action selection problem. The planning framework has been extended from the classical deterministic plan generation problem along many other dimensions, in particular nondeterministic actions. With the introduction of nondeterministic actions, the presence of an environment and other agents can become a consideration. In fact, actions may have nondeterministic effects not only because of the uncertainty of their own execution, but also due to the uncertainty of the actions of other agents. The possible presence of other agents as executors is the challenge of “multiagent planning.” The interest in this area has been steadily increasing and many issues remain open. Despite the existence of planning languages with explicit models of uncontrallable agents [Jensen and Veloso, 2000], we believe that there has not been a formal discussion of the space of multiagent plans or solutions. In this work, we do not focus on the problem of plan generation for multiagent planning. Instead, we focus on the interesting question of analyzing and comparing solutions for multiagent planning. Our motivation comes from making an analogy with game theory and the notion of equilibria [Owen, 1995]. Inspired by game theory and extending previous formal definitions of single-agent planning [Cimatti et al., 2000], in this paper, we introduce a formal definition of equilibria for multiagent planning.