Strategy Representation and Reasoning for Incomplete Information Concurrent Games in the Situation Calculus

Abstract

Strategy representation and reasoning for incomplete information concurrent games has recently received much attention in multi-agent system and AI communities. However, most of the logical frameworks are based on concrete game models, lack the abilities to reason about strategies explicitly or specify strategies procedurally, and ignore the issue of coordination within a coalition. In this paper, by a simple extension of a variant of multi-agent epistemic situation calculus with a strategy sort, we develop a general framework for strategy representation and reasoning for incomplete information concurrent games. Based on Golog, we propose a strategy programming language which can be conveniently used to specify collective strategies of coalitions at different granularities. We present a formalization of joint abilities of coalitions under commitments to strategy programs. Different kinds of individual strategic abilities can be distinguished in our framework. Both strategic abilities in ATL and joint abilities of Ghaderi et al. can be considered as joint abilities under special programs in our framework. We illustrate our work with a variant of Levesque's Squirrels World.