{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10555","name":"Information Value of Two-Prover Games","abstract":"We introduce a generalization of the standard framework for studying the difficulty of two-prover games. Specifically, we study the model where Alice and Bob are allowed to communicate (with information constraints) - in contrast to the usual two-prover game where they are not allowed to communicate after receiving their respective input. We study the trade-off between the information cost of the protocol and the achieved value of the game after the protocol. \r\nIn particular, we show the connection of this trade-off and the amortized behavior of the game (i.e. repeated value of the game).\r\nWe show that if one can win the game with at least (1 - \\epsilon)-probability by communicating at most \\epsilon bits of information, \r\nthen one can win n copies with probability at least 2^{-O(\\epsilon n)}. This gives an intuitive explanation why Raz's counter-example to strong parallel repetition [Raz2008] (the odd cycle game) is a counter-example to strong parallel repetition - one can win the odd-cycle game on a cycle of length $m$ by communicating O(m^{-2})-bits where m is the number of vertices.\r\n\r\nConversely, for projection games, we show that if one can win n copies with probability larger than (1-\\epsilon)^n,\r\nthen one can win one copy with at least (1 - O(\\epsilon))-probability by communicating O(\\epsilon) bits of information. \r\nBy showing the equivalence between information value and amortized value, we give an alternative direction for further works in studying amortized behavior of the two-prover games.\r\n\r\nThe main technical tool is the \"Chi-Squared Lemma\" which bounds the information cost of the protocol in terms of Chi-Squared distance,\r\ninstead of usual divergence. This avoids the square loss from using Pinsker's Inequality.","keywords":["Two Prover Game","Parallel Repetition","Odd-Cycle Game","Amortized Value of the Game"],"author":[{"@type":"Person","name":"Braverman, Mark","givenName":"Mark","familyName":"Braverman"},{"@type":"Person","name":"Ko, Young Kun","givenName":"Young Kun","familyName":"Ko"}],"position":12,"pageStart":"12:1","pageEnd":"12:15","dateCreated":"2018-01-12","datePublished":"2018-01-12","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Braverman, Mark","givenName":"Mark","familyName":"Braverman"},{"@type":"Person","name":"Ko, Young Kun","givenName":"Young Kun","familyName":"Ko"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2018.12","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/dx.doi.org\/10.1145\/2746539.2746565","http:\/\/arxiv.org\/abs\/1204.1505","http:\/\/dl.acm.org\/citation.cfm?id=1886521.1886577","http:\/\/arxiv.org\/abs\/1604.04340"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6297","volumeNumber":94,"name":"9th Innovations in Theoretical Computer Science Conference (ITCS 2018)","dateCreated":"2018-01-12","datePublished":"2018-01-12","editor":{"@type":"Person","name":"Karlin, Anna R.","givenName":"Anna R.","familyName":"Karlin"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10555","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6297"}}}