{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:17Z","timestamp":1760060417914,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:00:00Z","timestamp":1756425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>Hirshleifer\u2019s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective choice in conflict even when the contest is highly deterministic (i.e., with small noise). For that purpose, we establish two propositions on the contest with n\u22652 risk-neutral contestants under small noise. The first proposition states that every contestant bids arbitrarily close to zero (if not bidding zero with positive probability at all) under sufficiently small noise. The second proposition, more strikingly, states that every contestant either bids arbitrarily close to the second-highest valuation (among all the contestants\u2019 valuations), or simply remains passive with certainty under any sufficiently small noise. We further show that the first proposition holds for the contest between risk-averse individuals endowed with constant absolute risk aversion as well, and illustrate by an example how quickly polarization in bidding among contestants, as is predicted by the propositions, may emerge as the noise of the contest abates. These results help pave the way toward a complete characterization of the difference-form contest.<\/jats:p>","DOI":"10.3390\/g16050043","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T16:42:21Z","timestamp":1756485741000},"page":"43","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Power of Passivity in the Hirshleifer Contest Under Small Noise"],"prefix":"10.3390","volume":"16","author":[{"given":"Guang-Zhen","family":"Sun","sequence":"first","affiliation":[{"name":"Department of Economics, Faculty of Social Sciences, University of Macau, Macau 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s10058-007-0031-6","article-title":"Tullock and Hirshleifer: A meeting of the minds","volume":"11","author":"Alcalde","year":"2007","journal-title":"Review of Economic Design"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/S0176-2680(98)00032-9","article-title":"Difference-form contest success functions and effort levels in contests","volume":"14","author":"Baik","year":"1998","journal-title":"European Journal of Political Economy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/BF01211819","article-title":"The all-pay auction with complete information","volume":"8","author":"Baye","year":"1996","journal-title":"Economic Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1023\/A:1018345505969","article-title":"The incidence of overdissipation in rent-seeking contests","volume":"99","author":"Baye","year":"1999","journal-title":"Public Choice"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s11238-014-9425-4","article-title":"Relative difference contest success function","volume":"78","year":"2015","journal-title":"Theory and Decision"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Bevi\u00e1, C., and Corch\u03ccn, L. 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