We study a natural problem about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of that problem for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for three major classes of payoff functions: energy, discounted-sum, and mean-payoff.
@InProceedings{brice_et_al:LIPIcs.MFCS.2023.26, author = {Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie}, title = {{Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {26:1--26:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-292-1}, ISSN = {1868-8969}, year = {2023}, volume = {272}, editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.26}, URN = {urn:nbn:de:0030-drops-185608}, doi = {10.4230/LIPIcs.MFCS.2023.26}, annote = {Keywords: Games on graphs, Nash equilibria, subgame-perfect equilibria} }
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