Asymmetric contests with initial probabilities of winning

• Date: 01 December 2019
• DOI: http://doi.org/10.1111/ijet.12173
• Published date: 01 December 2019
• Author: Kyung Hwan Baik,Hanjoon Michael Jung

doi: 10.1111/ijet.12173

Asymmetric contests with initial probabilities of winning

Kyung Hwan Baik∗and Hanjoon Michael Jung†

We studycontests in which each player has an initial probability of winning the prize. First, we

consider a model in which the impact parameter is exogenous. Wefind that neither the number

of active players nor their identities nor the effort levels depend on the initial probabilities of

winning. Wefind also that the possibility that the winner is determined by the initial probabilities

of winning reduces prize dissipation, and tends to make most playersbetter off, compared to the

contest without this possibility. Then, considering a model in which the impact parameter is

endogenous, we find that every player may expend zero effort.

Key wor ds asymmetric contest, initial probability of winning, no-effort equilibrium, prize

dissipation, more efficient rent seeking

JEL classification D72, C72

Accepted 19 September 2017

1 Introduction

Westudy situations in which players are vested with their initial probabilities of winning a prize, and

compete with one another by expending irreversible effort to win the prize. Such contests with initial

probabilities of winning are readily observed but, to the best of our knowledge, have not previously

been studied.1Each player’sinitial probability of winning may reflect customs, institutional rules, her

natural talent, educational background, or previous efforts in the contest or other related contests.

For example, in a rent-seeking contest, it may reflect her relationship with government officials

established by her previous rent-seeking efforts. In an R&D contest, it may reflect her relevant

knowledge and experience gained from her previous R&D efforts. Finally, in a sporting contest,

it may reflect her natural talent or sporting skills (or ability) gained from her previous sporting

efforts.

∗Department of Economics, Sungkyunkwan University,Seoul 03063, South Korea,

†Ma Yinchu School of Economics,Tianjin University, Tianjin, China. Email: junghanjoon73@hanmail.net

Weare grateful to Sang-Kee Kim, Amy Baik Lee, Dan Kovenock, Wooyoung Lim, Eric Rasmusen, Jiabin Wu,two anony-

mous referees, an associateeditor and the managing editor of the journal, and seminar par ticipants at AcademiaSinica for

their helpful comments and suggestions. Earlier versions of this paper were presented at the 13th Annual Conference of

the Association for Public Economic Theory, Taipei, Taiwan,June 2012, and the 88th Annual Conference of the Western

Economic Association International, Seattle, WA, July 2013. Hanjoon Michael Jung gratefully acknowledges research

support from the National Science Council of the Republicof China (MOST 101-2410-H-001-014).

1A contest is defined as a situation in which players or contestants compete with one another by expending irreversible

effort or resources to win a prize. Examples of contests include rent-seeking contests, R&D contests, sporting contests,

election campaigns, litigation, tournaments, all-pay auctions, environmental conflicts, and arms races. Important work

in the literature on the theory of contests includes Tullock(1980), Dixit (1987), Hillman and Riley (1989), Epstein and

Nitzan (2007), and Konrad (2009).

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