Contests with endogenous deadlines

• Date: 01 March 2018
• Published date: 01 March 2018
• DOI: http://doi.org/10.1111/jems.12228

Received: 25 January 2017 Revised: 19 June 2017 Accepted: 7 September 2017

DOI: 10.1111/jems.12228

ORIGINAL ARTICLE

Contests with endogenous deadlines

Christian Seel

Maastricht University,

Department of Economics

(Email: c.seel@maastrichtuniversity.nl)

Abstract

This paper analyzes the problem of a contest designer who chooses a starting time and

a deadline of the contest to maximize discounted total effort by the contestants. Each

contestant secretly decides how much effort to exert between the starting time and the

deadline. At the deadline, the contestant who exerted most effort wins a prize, which

consists of the endowment of the designer and collected interest. The contest has a

unique Nash equilibrium. In the main model, the designer should announce the contest

immediately with a short deadline to promote intense competition. I analyze how the

optimal starting time and deadline change for a variable contest prize, different types

of asymmetries, a Tullocklotter y contestsuccess function, and different goal functions

of the designer.

1INTRODUCTION

Contests are frequently used to promote competition, both within firms and between firms or individuals. Many contests share

the same temporal structure: the designer chooses when to announce the competition and specifies the assessment rules, the

deadline, and the winner prize. All contestants can exert effort between the announcement and the deadline, at which the best

performing contestant receives the prize.

Let me provide a few examples, which fit the above description to discuss the scope of this paper. For instance, at schools

or universities, the teacher announces the day and the importance of the test and the students decide when and how much they

study. The best grade within their peer group is the “prize,” which yields prestige and might facilitate applications for the next

higher career level or scholarships. The teacher/schoolfaces the following problems: When should the test be written (deadline)?

When should the teacher announce the date of the test (starting time)? How does the answer depend on the objective function

of the teacher?

In big law firms, promotion decisions are often taken in the form of a contest, that is, several associates compete for the prize

of becoming a partner. In this example, the starting time and prize are given by the beginning of the contract and the value of

becoming a partner, respectively. Thus, the relevant question is when the firm should take the “making partner” decision.

As a final example, consider an innovation contest, forexample, for improving a search algorithm. The designer faces a trade-

off between the expected quality of the algorithm and the deadline of the contest, which is the first date at which she can use it.

Thus, she needs to find the starting time/deadline/prize schedule, which maximizes her objective function.

The literature on the optimal duration in contests, however, is very scarce. Contest models such as all-pay auctions or Tul-

lock contests do not model the time dimension at all, whereas other contest models with unobservable actions abstract from

discounting and/or assume infinite or exogenous deadlines.1

Instead, this paper treats the contest length as a choice variable of the designer. During the contest stage, participants decide

when to exert effort, but cannot observe the rival's effort decisions, that is, their interaction remains static. Equilibrium properties

I am indebted to Alex Gershkov and Paul Schweinzerfor a myriad of inspiring discussions. Moreover, I would like to thank the reviewers, Philipp Denter,Jörg

Franke, Bart Golsteyn, Diego Moreno, Frank Riedel, Nora Szech, Peter Werner, and seminar audiences in Bielefeld, Karlsruhe, Maastricht, and Madrid for

valuable remarks and suggestions.

J Econ Manage Strat. 2018;27:119–133. © 2017 WileyPeriodicals, Inc. 119wileyonlinelibrary.com/journal/jems