Average-energy games

• Published in: Acta informatica 2018-03, Vol.55 (2), p.91-127
• Main Authors: Bouyer, Patricia, Markey, Nicolas, Randour, Mickael, Larsen, Kim G., Laursen, Simon
• Format: Article
• Language: English
• Subjects: Computer Science; Computer Science and Game Theory; Computer Systems Organization and Communication Networks; Controllers; Data Structures and Information Theory; Energy; Energy conservation; Energy storage; Formal Languages and Automata Theory; Game theory; Information Systems and Communication Service; Logic in Computer Science; Logics and Meanings of Programs; Multiagent Systems; Original Article; Software Engineering/Programming and Operating Systems; Theory of Computation
• ISSN: 0001-5903; 1432-0525
• DOI: 10.1007/s00236-016-0274-1

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the objective is to optimize the long-run average gain per action, and energy games, where the system has to avoid running out of energy. We study average-energy games, where the goal is to optimize the long-run average of the accumulated energy. We show that this objective arises naturally in several applications, and that it yields interesting connections with previous concepts in the literature. We prove that deciding the winner in such games is in NP ∩ coNP and at least as hard as solving mean-payoff games, and we establish that memoryless strategies suffice to win. We also consider the case where the system has to minimize the average-energy while maintaining the accumulated energy within predefined bounds at all times: this corresponds to operating with a finite-capacity storage for energy. We give results for one-player and two-player games, and establish complexity bounds and memory requirements.