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Energy Mean-Payoff Games Bruyère, Véronique Hautem, Quentin Randour, Mickael Raskin, Jean-François two-player zero-sum games played on graphs energy and mean-payoff objectives complexity study and construction of optimal strategies 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Véronique Bruyère and Quentin Hautem and Mickael Randour and Jean-François Raskin 2019 Is Part Of LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2019.21 urn:nbn:de:0030-drops-109239 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.21 eng https://creativecommons.org/licenses/by/3.0/legalcode