{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T20:46:26Z","timestamp":1786999586885,"version":"build-2736575974"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T00:00:00Z","timestamp":1740614400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2026,6]]},"abstract":"\n We study minimax regret treatment rules under\n matched treatment assignment<\/jats:italic>\n in a setup where a policymaker, informed by a sample of size\n N<\/jats:italic>\n , needs to decide between\n T<\/jats:italic>\n different treatments for a\n \n \n \n T<\/mml:mi>\n \u2265<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:math>\n $T\\geq 2$<\/jats:tex-math>\n \n upper T greater than or equals 2<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . Randomized rules are allowed for. We show that the generalization of the minimax regret rule derived in Schlag (2006,\n ELEVEN\u2014Tests needed for a recommendation<\/jats:italic>\n , EUI working paper) and Stoye (2009,\n Journal of Econometrics<\/jats:italic>\n 151, 70\u201381) for the case\n \n \n \n T<\/mml:mi>\n =<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:math>\n $T=2$<\/jats:tex-math>\n \n upper T equals 2<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is minimax regret for general finite\n \n \n \n T<\/mml:mi>\n ><\/mml:mo>\n 2<\/mml:mn>\n <\/mml:math>\n $T>2$<\/jats:tex-math>\n \n upper T greater than 2<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and also that the proof structure via the Nash equilibrium and the \u201ccoarsening\u201d approaches generalizes as well. We also show by example, that in the case of\n random assignment<\/jats:italic>\n the generalization of the minimax rule in Stoye (2009,\n Journal of Econometrics<\/jats:italic>\n 151, 70\u201381) to the case\n \n \n \n T<\/mml:mi>\n ><\/mml:mo>\n 2<\/mml:mn>\n <\/mml:math>\n $T>2$<\/jats:tex-math>\n \n upper T greater than 2<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is not necessarily minimax regret and derive minimax regret rules for a few small sample cases, e.g., for\n \n \n \n N<\/mml:mi>\n =<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:math>\n $N=2$<\/jats:tex-math>\n \n upper N equals 2<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n when\n \n \n \n T<\/mml:mi>\n =<\/mml:mo>\n 3.<\/mml:mn>\n <\/mml:math>\n $T=3.$<\/jats:tex-math>\n \n upper T equals 3 period<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n <\/jats:p>\n \n In the case where a covariate\n x<\/jats:italic>\n is included, it is shown that a minimax regret rule is obtained by using minimax regret rules in the \u201cconditional-on-\n x<\/jats:italic>\n \u201d problem if the latter are obtained as Nash equilibria.\n <\/jats:p>","DOI":"10.1017\/s0266466625000040","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T04:46:55Z","timestamp":1740631615000},"page":"723-749","source":"Crossref","is-referenced-by-count":2,"title":["A NOTE ON MINIMAX REGRET RULES WITH MULTIPLE TREATMENTS IN FINITE SAMPLES"],"prefix":"10.1017","volume":"42","author":[{"given":"Haoning","family":"Chen","sequence":"first","affiliation":[{"name":"Pennsylvania State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4395-5390","authenticated-orcid":false,"given":"Patrik","family":"Guggenberger","sequence":"additional","affiliation":[{"name":"Pennsylvania State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,2,27]]},"reference":[{"key":"S0266466625000040_r16","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00530.x"},{"key":"S0266466625000040_r29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.06.012"},{"key":"S0266466625000040_r1","doi-asserted-by":"crossref","unstructured":"Aradillas Fern\u00e1ndez, A. , Blanchet, J. , Montiel Olea, J. 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