Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Economics of Governance
Published in: Economics of Governance 2/2019

18-03-2019 | Original Paper

Step-by-step group contests with group-specific public-good prizes

Author: Katsuya Kobayashi

Published in: Economics of Governance | Issue 2/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The achievements reached by group members’ effort, which accompanies the possibility of members’ free-riding, affect the outcomes of competition among groups. In some cases, each achievement has the binary characteristic of “one or nothing.” For example, research groups face the challenge of making a scientific finding or not. The groups compete for a scientific breakthrough by making the related findings in a “step-by-step” manner. One finding could fail because of a mistake caused by a slight lack of effort by one member. Such a characteristic of “one or nothing” motivates group members without any incentive scheme. This study analyzes group contests with group-specific public-good prizes, in which we introduce a step function with the characteristics of “one or nothing” and “step-by-step” as a group impact function. We show the existence of the Nash equilibrium at which no group member free-rides on the others and at which more achievements than those reachable by a single member are reached.
previous article Selection rates and bureaucratic performance

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Footnotes
1
The process of making findings would bring the group members skills and expertise to attain a breakthrough earlier than rival groups. In addition, their publications on these findings would provide credibility to their breakthrough.
 
2
See the detailed explanation at www.​nobelprize.​org.
 
3
Chowdhury and Topolyan (2016) summarize these studies.
 
4
See also the original works of Hirshleifer (1983; 1985).
 
5
With regard to the coalition-proof Nash equilibrium, Bernheim et al. (1987) originally defined the equilibrium concept. However, the coalition-proof Nash equilibrium of Lee (2012) and Chowdhury and Topolyan (2016) is different from the original concept of Bernheim et al. (1987). Quartieri and Shinohara (2016) provide the details of the difference and redefine the equilibrium concept of Lee (2012) as the group-proof Nash equilibrium.
 
6
In other words, we employ the Tullock-form contest success function (Tullock 1980).
 
7
We allow that, in each group, some members’ valuations are equal to or higher than the costs of achievement, namely \(v_j^i \ge m_k\), and the others have lower valuations, namely \(v_h^i< m_k\), \(h \ne j\).
 
8
This is the same definition as the contest success function for group i in Baik (2008).
 
9
This assumption does not affect the following results intrinsically. We obtain the same results even if any group obtains nothing when \(X_i = 0\) and \(f(X_i)=0\) for all i. See also the Introduction of Quartieri and Shinohara (2016).
 
10
If j expends any effort less than \(x_j^i\), j has to pay this effort cost on the same achievement level \(\alpha - 1\). Thus, in this case, j expends nothing.
 
11
The results of Baik (2008) depend on the assumption of an individual constant marginal cost of effort. If we assume an increasing marginal cost of effort in Baik’s model, members with small valuations also expend effort at the Nash equilibrium. Then, the reachable achievement level is the one at the equilibrium. While our model has the same individual constant marginal cost of effort as Baik (2008), the Nash equilibria contain the characteristics that anyone can expend effort because of the step-by-step structure. In addition, multiple reachable achievement levels can exist at the Nash equilibria, as we show in the following.
 
12
Regarding the discrete public good, Palfrey and Rosenthal (1984; 1988), Gradstein (1994) and Menezes et al. (2001) are instructive works.
 
13
Even if we assume that no group obtains anything when \(X_i=0\) for all i, j does not deviate from \(x_j^i=0\) because \(m_1> v_j^i> x_j^i > 0\).
 
14
In competition in research, for example, the principal is a professor and the agents are her group members such as research fellows, research assistants, and graduate students.
 
15
The reward must cover the cost of stepping up from the default achievement level \(\alpha ^*-t\) to the target level \(\alpha ^*\): \(\displaystyle b_j^i \ge \frac{v_j^i}{\sum _{j=1}^{n_i}v_j^i} \sum _{k=\alpha ^*-t+1}^{\alpha ^*} m_k - \frac{t \beta }{(\alpha ^* + \beta )(\alpha ^*-t+\beta )} v^i_j\). The first term on the right-hand side is the cost shared by Expense Rule A. The second term is the rise in expected valuation brought about by this step up. Here, the default achievement level \(\alpha ^* - t\) viewed as a reservation is any reachable achievement level at Nash equilibria under the individual decisions.
 
16
If (2) is non-negative only in \((\alpha , \beta ) = (1,1)\), both cases are at the same level at a Nash equilibrium.
 
17
See Bernheim et al. (1987) and Quartieri and Shinohara (2016) for the strict definitions of the coalition-proof Nash equilibrium and group-proof Nash equilibrium, respectively.
 
18
Chowdhury and Topolyan (2016) use a concept with a similarity of the group-proof Nash equilibrium as their coalition-proof equilibrium. However, they do not share the concepts of Bernheim et al. (1987) or Quartieri and Shinohara (2016).
 
Literature
Baik KH (2008) Contests with group-specific public-good prizes. Soc Choice Welf 30:103–117CrossRef
Baik KH, Kim IG, Na S (2001) Bidding for a group-specific public-good prize. J Public Econ 82:415–429CrossRef
Bernheim BD, Peleg B, Whinston MD (1987) Coalition-proof Nash equilibria I. Concepts. J Econ Theory 42:1–12CrossRef
Chowdhury SM, Lee D, Sheremeta RM (2013) Top guns may not fire: best-shot group contests with group-specific public good prizes. J Econ Behav Organ 92:94–103CrossRef
Chowdhury SM, Topolyan I (2016) The attack-and-defense group contests: best shot versus weakest link. Econ Inquiry 54–1:548–557CrossRef
Dijkstra BR (1998) Cooperation by way of support in a rent seeking contest for a public good. Eur J Polit Econ 14:703–725CrossRef
Gradstein M (1994) Efficient provision of a discrete public good. Int Econ Rev 35:877–897CrossRef
Hirshleifer J (1983) From weakest-link to best-shot: the voluntary provision of public goods. Public Choice 41:371–386CrossRef
Hirshleifer J (1985) From weakest-link to best-shot: correction. Public Choice 46:221–223CrossRef
Katz E, Nitzan S, Rosenberg J (1990) Rent-seeking for pure public goods. Public Choice 65:49–60CrossRef
Lee D (2012) Weakest-link contests with group-specific public good prizes. Eur J Polit Econ 28:238–248CrossRef
Menezes FM, Monteiro PK, Temini A (2001) Private provision of discrete public goods with incomplete information. J Math Econ 35:493–514CrossRef
Palfrey T, Rosenthal H (1984) Participation and the provision of discrete public goods: a strategic analysis. J Public Econ 24:171–193CrossRef
Palfrey T, Rosenthal H (1988) Private incentives in social dilemmas: the effects of incomplete information and altruism. J Public Econ 35:309–332CrossRef
Quartieri F, Shinohara R (2016) Two-group contests with communication within and between groups. In: von Mouche P, Quartieri F (eds) Equilibrium theory for Cournot oligopolies and related games—essays in honour of Koji Okuguchi, Springer, pp 245–268
Riaz K, Shogren JF, Johnson SR (1995) A general model of rent seeking for public goods. Public Choice 82:243–259CrossRef
Takahashi K, Tanabe K, Ohnuki M, Narita M, Ichisaka T, Tomoda K, Yamanaka S (2007) Induction of pluripotent stem cells from adult human fibroblasts by defined factors. Cell 131–5:861–872CrossRef
Takahashi K, Yamanaka S (2006) Induction of pluripotent stem cells from mouse embryonic and adult fibroblast cultures by defined factors. Cell 126–4:663–676CrossRef
Topolyan I (2014) Rent-seeking for a public good with additive contributions. Soc Choice Welf 42:465–476CrossRef
Tullock G (1980) Efficient rent seeking. In: Buchanan JM, Tollison RD, Tullock G (eds) Toward a theory of the rent-seeking society. Texas A&M University Press, College Station, pp 97–112
Ursprung HW (1990) Public goods, rent dissipation, and candidate competition. Econ Polit 2:115–132CrossRef
Yu J, Vodyanik MA, Smuga-Otto K, Antosiewicz-Bourget J, Frane JL, Tian S, Nie J, Jonsdottir GA, Ruotti V, Stewart R, Slukvin II, Thomson JA (2007) Induced pluripotent stem cell lines derived from human somatic cells. Science 318–5858:1917–1920CrossRef
Metadata
Title
Step-by-step group contests with group-specific public-good prizes
Author
Katsuya Kobayashi
Publication date
18-03-2019
Publisher
Springer Berlin Heidelberg
Published in
Economics of Governance / Issue 2/2019
Print ISSN: 1435-6104
Electronic ISSN: 1435-8131
DOI
https://doi.org/10.1007/s10101-019-00224-4

Premium Partner

    Image Credits