Game−Theoretic Reasoning About Actions in Nonmonotonic Causal Theories

Abstract

We present the action language GC+ for reasoning about actions in multi-agent systems under probabilistic uncertainty and partial observability, which is an extension of the action language C+ that is inspired by partially observable stochastic games (POSGs). We provide a finite-horizon value iteration for this framework and show that it characterizes finite-horizon Nash equilibria. We also describe how the framework can be implemented on top of nonmonotonic causal theories. We then present acyclic action descriptions in GC+ as a special case where transitions are computable in polynomial time. We also give an example that shows the usefulness of our approach in practice.