Traditionally quantitative games such as mean-payoff games and discount sum games have two players - one trying to maximize the payoff, the other trying to minimize it. The associated decision problem, "Can Eve (the maximizer) achieve, for example, a positive payoff?" can be thought of as one player trying to attain a payoff in the interval (0,infinity). In this paper we consider the more general problem of determining if a player can attain a payoff in a finite union of arbitrary intervals for various payoff functions (liminf/limsup, mean-payoff, discount sum, total sum). In particular this includes the interesting exact-value problem, "Can Eve achieve a payoff of exactly (e.g.) 0?"
@InProceedings{hunter_et_al:LIPIcs.FSTTCS.2014.365, author = {Hunter, Paul and Raskin, Jean-Francois}, title = {{Quantitative Games with Interval Objectives}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {365--377}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.365}, URN = {urn:nbn:de:0030-drops-48569}, doi = {10.4230/LIPIcs.FSTTCS.2014.365}, annote = {Keywords: Quantitative games, Mean-payoff games, Discount sum games} }
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