Energy mean-payoff games

Abstract

In this paper, we study one-player and two-player energy mean-payoff games. Energy mean-payoff games are games of infinite duration played on a finite graph with edges labeled by 2-dimensional weight vectors. The objective of the first player (the protagonist) is to satisfy an energy objective on the first dimension and a mean-payoff objective on the second dimension. We show that optimal strategies for the first player may require infinite memory while optimal strategies for the second player (the antagonist) do not require memory. In the one-player case (where only the first player has choices), the problem of deciding who is the winner can be solved in polynomial time while for the two-player case we show co-NP membership and we give effective constructions for the infinite-memory optimal strategies of the protagonist. ACM Subject ClassificationSoftware and its engineering → Formal methods; Theory of computation → Logic and verification; Theory of computation → Solution concepts in game theory Keywords and phrases two-player zero-sum games played on graphs, energy and mean-payoff objectives, complexity study and construction of optimal strategies Digital Object Identifier 10.4230/LIPIcs...