Crowdsourcing contests with entry cost

• Author: Gongbing Bi,Lindong Liu,Xu Tian,Xiaobei Shen
• Published date: 01 May 2021
• Date: 01 May 2021
• DOI: http://doi.org/10.1111/itor.12883

Intl. Trans. in Op. Res. 28 (2021) 1371–1392

DOI: 10.1111/itor.12883

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Crowdsourcing contests with entry cost

Xu Tian , Gongbing Bi , Xiaobei Shen and Lindong Liu∗

School of Management, University of Science and Technology of China, Hefei,Anhui 230026, P.R. China

E-mail: hi142434@mail.ustc.edu.cn [Tian]; bigb@ustc.edu.cn [Bi]; fayshen@ustc.edu.cn [Shen];

ldliu@ustc.edu.cn [Liu]

Received 29 February2020; received in revised form 8 August 2020; accepted 18 September 2020

Abstract

Today, companies can seek solutions to businessproblems by sponsoring cocreation activities such as crowd-

sourcing contests. This paper studies a crowdsourcing contest in which a sponsor seeks solutions from a

number of independent contestants.Specifically, we reveal howthe number of contestants affects the expected

effort and maximum quality in a crowdsourcing contest. First, we show that an effort-decreasing effect ex-

ists for any number of winners when there are a number of contestants, while an effort-increasing effect may

occur when there are relatively few contestants. Second, we find that the expected maximum quality at most

concavely increases with the number of contestants. Finally, we extend the analysis to the case with a flexible

number of contributors.Our results imply that a restricted-entry policy should be adopted if the entry cost is

considered, which is not observed in the prior literature.

Keywords:crowdsourcing contests; incentive; entry policy; random shock

1. Introduction

In recent years, new business models that harness the productivity and creativity of the Internet

community have proliferated. Among them, crowdsourcing is one of the most attractive models

adopted by firms (sponsors) seeking solutions from a large group of Internet users (contestants)

(Bockstedt et al., 2016; Wooten and Ulrich, 2017; Chen et al., 2018). There are several well-known

crowdsourcingplatforms worldwide, including InnoCentiveand TopCoder in the United States and

Taskcn and EPWK in China, and their services are in great demand. For example, up to June 2018,

EPWK, which provides different services for firms, had organized 7,583,280 tasks with total awards

of CNY 16,445,823,379 (approximately USD 2.4 billion) and attracted 18,833,266 registered users.

On most crowdsourcing platforms, crowdsourcing contests and their variants are organized by the

sponsor. These contests provide effective solutions to challenging projects. Thus, it is of great im-

portance to explore the optimal design of crowdsourcing contests.

∗Corresponding author.

© 2020 The Authors.

International Transactionsin Operational Research © 2020 International Federation of OperationalResearch Societies

Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148,

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1372 X. Tian et al. / Intl. Trans. in Op. Res. 28 (2021) 1371–1392

To run a crowdsourcing contest, a sponsor must first announce to the contestants the following:

an innovation-related project, an award scheme, and an entry policy. Typically, the award scheme

specifies the number of winners and the award amount allocated to each winner. An award scheme

selecting just one winner is referred to as a single-winner award scheme, and the winner collects

the entire award (also named a winner-takes-all scheme in Ales et al., 2017b). An award scheme

allowing more than one winner is called a multiple-winner award scheme and the sponsor fairly al-

locates the award among the winners. The entry policy specifies the number of contestants allowed

to participate in the contest. When a free-entry policy (see Ales et al., 2017a) is adopted, there is no

restriction on the number of participants in the contest. However, sometimes, it is worthwhile to

apply a restricted-entry policy (see Taylor, 1995). Such a policy restricts the number of participants

to provide the sponsor with higher welfare. According to the announced award scheme, the con-

testants decide whether to participate, and each participating contestant results in a solution of a

certain quality depending on the effort expended and a random shock. The sponsor then evaluates

and ranks the solutions and, finally, awards the winners according to the award scheme.

To encourage the contestants to participate, the sponsor needs to incur some advertising costs.

In the evaluation process, it also incurs some evaluation costs. These constitute the entry cost for a

crowdsourcing contest. As weshow later in the main context, restricting the number of participants

in a crowdsourcing contest can mean a more realistic entry policy if the entry cost is considered.

In this paper, we investigate the question regarding how the number of contestants affects the

expected effort and maximum quality in a crowdsourcing contest, and provide the practical entry

policy. The question is critical to contest mechanism design and has received some attention in the

literature. Next, we review some related studies and clarify our main contributions.

The two most frequently used criteria for quantifying the expected quality are the expected aver-

age quality (EAQ) and the expected maximum quality (EMQ), both are of practical importance, for

example, Kalra and Shi (2001), Moldovanu and Sela (2001), Hu and Wang (2020), and Körpeo˘

glu

and Cho (2017). Several theoretical studies (see, e.g., Taylor, 1995; Fullerton and McAfee, 1999;

Che and Gale, 2003) show thatthe EAQ-based model is always associated with an effort-decreasing

effect in which the contestant tends to expend less effort when there are more participants. This

finding implies that the restricted-entry policy is preferred for the sake of high EAQ. In addition,

Boudreau et al. (2011) empirically prove their results. If the sponsor cares about EMQ, Ales et al.

(2017a) show that a free-entry policy is optimal for a crowdsourcing contest when the quality un-

certainty of contestants’ solutions is sufficiently large or the sponsor benefits from a number of

contributors whose solutions are beneficial to EMQ.

To reveal the generality of our analysis, we consider the impacts of the number of allowed partic-

ipants on both EAQ and EMQ under various practical situations. In our main results, we find that

the effort-decreasing effect may not hold in the EAQ-based model when there are a small number

of contestants. More surprisingly, the free-entry policy is always suboptimal, rather than optimal as

was claimed in Ales et al. (2017a), according to the EMQ-based model when the entry cost exists.

Based on a general contest model, we derive some new and practical results that have not been

revealed in the existing crowdsourcing contest literature. Our main contributions are summarized

as follows.

1. We show that an effort-decreasing effect does exist for any number of winners when the number

of contestants is sufficiently large. Otherwise, more interestingly, the effort-increasing effect may

© 2020 The Authors.

International Transactionsin Operational Research © 2020 International Federation of OperationalResearch Societies