[ { "id": "https://authors.library.caltech.edu/records/yrhbn-2yz42", "eprint_id": 94488, "eprint_status": "archive", "datestamp": "2023-08-19 14:14:47", "lastmod": "2026-03-31 05:23:01", "type": "publication_workingpaper", "metadata_visibility": "show", "creators": { "items": [ { "id": "Pomatto-L", "name": { "family": "Pomatto", "given": "Luciano" }, "orcid": "0000-0002-4331-8436" }, { "id": "Strack-P", "name": { "family": "Strack", "given": "Philipp" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "The cost of information", "ispublished": "unpub", "full_text_status": "public", "note": "We thank Kim Border, Ben Brooks, Simone Cerreia-Vioglio, Tommaso Denti, Federico Echenique, Drew Fudenberg, Ed Green, Adam Kapor, Massimo Marinacci, Jeffrey Mensch, Filip Matejka, Stephen Morris, and Doron Ravid for their comments. All errors and omissions are our own. \n\nOmer Tamuz was supported by a grant from the Simons Foundation (#419427).\n\n

Accepted Version - cost_of_information.pdf

Submitted - 1812.04211.pdf

", "abstract": "We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with a monotonicity and a continuity conditions, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states. We argue that this cost function is a versatile modeling tool that leads to more realistic predictions than mutual information.", "date": "2019-02-04", "date_type": "published", "id_number": "CaltechAUTHORS:20190404-161816718", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190404-161816718", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1812.04211", "primary_object": { "basename": "1812.04211.pdf", "url": "https://authors.library.caltech.edu/records/yrhbn-2yz42/files/1812.04211.pdf" }, "related_objects": [ { "basename": "cost_of_information.pdf", "url": "https://authors.library.caltech.edu/records/yrhbn-2yz42/files/cost_of_information.pdf" } ], "pub_year": "2019", "author_list": "Pomatto, Luciano; Strack, Philipp; et al." }, { "id": "https://authors.library.caltech.edu/records/2qapf-ext21", "eprint_id": 71968, "eprint_status": "archive", "datestamp": "2023-08-19 10:42:50", "lastmod": "2026-04-10 01:21:47", "type": "publication_workingpaper", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Lima-Y", "name": { "family": "Lima", "given": "Yuri" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "An Abramov formula for stationary spaces of discrete groups", "ispublished": "unpub", "full_text_status": "public", "keywords": "Abramov formula, Furstenberg entropy, random walk, random walk entropy, stationary space", "note": "Date: April 25, 2012. \n\nSubmitted on 24 Apr 2012. \n\nYuri Lima is supported by the European Research Council, grant 239885. Omer Tamuz is supported by ISF grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing, and this research is supported in part by this Google Fellowship.\n\n

Submitted - 1204.5414.pdf

", "abstract": "Let (G, \u03bc) be a discrete group equipped with a generating probability measure, and let \u0393 be a finite index subgroup of G. A \u03bc-random walk on G, starting from the identity, returns to \u0393 with probability one. Let \u03b8 be the hitting measure, or the distribution of the position in which the random walk first hits \u0393.\nWe prove that the Furstenberg entropy of a (G, \u03bc)-stationary space, with respect to the induced action of (\u0393, \u03b8), is equal to the Furstenberg entropy with respect to the action of (G, \u03bc), times the index of \u0393 in G. The index is shown to be equal to the expected return time to \u0393.\nAs a corollary, when applied to the Furstenberg-Poisson boundary of (G, \u03bc), we prove that the random walk entropy of (\u0393, \u03b8) is equal to the random walk entropy of (G, \u03bc), times the index of \u0393 in G.", "date": "2012-04-24", "date_type": "published", "id_number": "CaltechAUTHORS:20161114-064703507", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-064703507", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "239885" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1204.5414", "primary_object": { "basename": "1204.5414.pdf", "url": "https://authors.library.caltech.edu/records/2qapf-ext21/files/1204.5414.pdf" }, "pub_year": "2012", "author_list": "Hartman, Yair; Lima, Yuri; et al." } ]