{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T22:59:26Z","timestamp":1773097166535,"version":"3.50.1"},"reference-count":48,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Management Science"],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:p> In standard models of iterative thinking, players choose a fixed rule level from a fixed rule hierarchy. Nonequilibrium behavior emerges when players do not perform enough thinking steps. Existing approaches, however, are inherently static. This paper introduces a Bayesian level-k model, in which level-0 players adjust their actions in response to historical game play, whereas higher-level thinkers update their beliefs on opponents\u2019 rule levels and best respond with different rule levels over time. As a consequence, players choose a dynamic rule level (i.e., sophisticated learning) from a varying rule hierarchy (i.e., adaptive learning). We apply our model to existing experimental data on three distinct games: the p-beauty contest, Cournot oligopoly, and private-value auction. We find that both types of learning are significant in p-beauty contest games, but only adaptive learning is significant in the Cournot oligopoly, and only sophisticated learning is significant in the private-value auction. We conclude that it is useful to have a unified framework that incorporates both types of learning to explain dynamic choice behavior across different settings. <\/jats:p><jats:p> This paper was accepted by Manel Baucells, decision analysis. <\/jats:p>","DOI":"10.1287\/mnsc.2020.3595","type":"journal-article","created":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T14:48:07Z","timestamp":1596725287000},"page":"1622-1638","source":"Crossref","is-referenced-by-count":15,"title":["A Bayesian Level-<i>k<\/i> Model in <i>n<\/i>-Person Games"],"prefix":"10.1287","volume":"67","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-5210-4977","authenticated-orcid":false,"given":"Teck-Hua","family":"Ho","sequence":"first","affiliation":[{"name":"National University of Singapore, Singapore 119077;"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-1576-5666","authenticated-orcid":false,"given":"So-Eun","family":"Park","sequence":"additional","affiliation":[{"name":"University of British Columbia, Vancouver, British Columbia V6T1Z2, Canada;"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-4862-3074","authenticated-orcid":false,"given":"Xuanming","family":"Su","sequence":"additional","affiliation":[{"name":"University of Pennsylvania, Philadelphia, Pennsylvania 19104"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdv052"},{"issue":"5","key":"B2","first-page":"1178","volume":"75","author":"Binmore K","year":"1985","journal-title":"Amer. 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