The Power of Passivity in the Hirshleifer Contest Under Small Noise

Guang-Zhen Sun ()
Additional contact information
Guang-Zhen Sun: Department of Economics, Faculty of Social Sciences, University of Macau, Macau 999078, China

Games, 2025, vol. 16, issue 5, 1-20

Abstract: Hirshleifer’s 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 ≥ 2 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’ 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.

Keywords: difference-form contest; passivity; Nash equilibrium; small noise; all-pay auction (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2073-4336/16/5/43/pdf (application/pdf)
https://www.mdpi.com/2073-4336/16/5/43/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:16:y:2025:i:5:p:43-:d:1737630

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().