Signaling games for log-concave distributions: Number of bins and properties of equilibria

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buir.contributor.authorSarıtaş, Serkan
buir.contributor.authorGezici, Sinan
dc.contributor.authorKazıklı, E.
dc.contributor.authorSarıtaş, Serkan
dc.contributor.authorGezici, Sinan
dc.contributor.authorLinder, T.
dc.contributor.authorYüksel, S.
dc.date.accessioned2022-01-31T06:42:35Z
dc.date.available2022-01-31T06:42:35Z
dc.date.issued2021-11-25
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description( Early Access )en_US
dc.description.abstractWe investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown that the number of bins in any equilibrium has to be countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on [0, 1]. In this paper, we first refine this result in the context of log-concave sources. For sources with two-sided unbounded support, we prove that, for any finite number of bins, there exists a unique equilibrium. In contrast, for sources with semi-unbounded support, there may be a finite upper bound on the number of bins in equilibrium depending on certain conditions stated explicitly. Moreover, we prove that for log-concave sources, the expected costs of the encoder and the decoder in equilibrium decrease as the number of bins increases. Furthermore, for strictly log-concave sources with two-sided unbounded support, we prove convergence to the unique equilibrium under best response dynamics which starts with a given number of bins, making a connection with the classical theory of optimal quantization and convergence results of Lloyd’s method. In addition, we consider more general sources which satisfy certain assumptions on the tail(s) of the distribution and we show that there exist equilibria with infinitely many bins for sources with two-sided unbounded support. Further explicit characterizations are provided for sources with exponential, Gaussian, and compactly-supported probability distributions.en_US
dc.description.provenanceSubmitted by Evrim Ergin (eergin@bilkent.edu.tr) on 2022-01-31T06:42:35Z No. of bitstreams: 1 Signaling_games_for_log-concave_distributions_Number_of_bins_and_properties_of_equilibria.pdf: 591405 bytes, checksum: 1543d7271de0483bfc27a73119e6cde2 (MD5)en
dc.description.provenanceMade available in DSpace on 2022-01-31T06:42:35Z (GMT). No. of bitstreams: 1 Signaling_games_for_log-concave_distributions_Number_of_bins_and_properties_of_equilibria.pdf: 591405 bytes, checksum: 1543d7271de0483bfc27a73119e6cde2 (MD5) Previous issue date: 2021-11-25en
dc.identifier.doi10.1109/TIT.2021.3130672en_US
dc.identifier.eissn1557-9654
dc.identifier.issn0018-9448
dc.identifier.urihttp://hdl.handle.net/11693/76896
dc.language.isoEnglishen_US
dc.publisherIEEEen_US
dc.relation.isversionofhttps://doi.org/10.1109/TIT.2021.3130672en_US
dc.source.titleIEEE Transactions on Information Theoryen_US
dc.subjectCheap talken_US
dc.subjectSignaling gamesen_US
dc.subjectNash equilibriumen_US
dc.subjectOptimal quantizationen_US
dc.subjectLloyd–Max algorithmen_US
dc.subjectPayoff dominant equilibriaen_US
dc.titleSignaling games for log-concave distributions: Number of bins and properties of equilibriaen_US
dc.typeArticleen_US

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