Advances in Contests

Paper Session

Friday, Jan. 6, 2017 10:15 AM – 12:15 PM

Hyatt Regency Chicago, Michigan 1A & 1B
Hosted By: American Economic Association
  • Chair: Ron Siegel, Pennsylvania State University

Pareto Improvements in the Contest for College Admissions

Wojciech Olszewski
,
Northwestern University
Ron Siegel
,
Pennsylvania State University

Abstract

We model high school students’ competition for college admissions as an all-pay contest with many players and prizes, and investigate how reducing the information revealed to colleges about students’performance can improve students’ welfare in a Pareto sense. Less information reduces the assortativity of the resulting matching, which reduces welfare, but also mitigates competition and reduces student effort, which increases welfare. We characterize the Pareto frontier of Pareto improving policies, and also identify improvements that are robust to the distribution of college seats and students’ utilities from the same. We apply our results to data from the National Longitudinal Survey of Youth to identify Pareto improving policies in the United States.

All-Pay Auctions With Ties

Alan Gelder
,
Chapman University
Dan Kovenock
,
Chapman University
Brian Roberson
,
Purdue University

Abstract

We study the symmetric, two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Thus players engage in competition over two margins: losing versus tying, and tying versus winning. Two pertinent parameters are the margin required for victory, and the value of tying relative to winning. We fully characterize the set of Nash equilibria for the entire parameter space. For much of the parameter space, there is a unique Nash equilibrium which is also symmetric. Equilibria typically involve randomizing over multiple disjoint intervals, so that in essence players randomize between attempting to tie and attempting to win. In equilibrium, expected bids and payoffs are non-monotonic in both the margin required for victory and the relative value of tying.

'Risk-Taking in Contests-The Impact of Fund-Manager Compensation on Investor Welfare

Philipp Strack
,
Berkeley University

Abstract

We analyze the effect of different patent protection policies in a dynamic perpetual race. Each firm continuously decides how much to invest in R&D to improve their technology. At any point in time,<br />
the firm with the better technology receives a higher market share and higher profits. <br />
We characterize equilibrium R&D efforts as a function of the strength of patent protection, i.e., the rate at which a firm is allowed to use technologies developed by the rival firm. The effort-maximizing patent protection level is typically intermediate and we discuss its relation to industry-specific parameters such as the speed and randomness of research progress.

Ranking Disclosure Policies in All-Pay Auctions With Incomplete Information

Jingfeng Lu
,
National University of Singapore
Hongkun Ma
,
National University of Singapore
Zhe Wang
,
National University of Singapore

Abstract

In this paper, we study information disclosure policies in all-pay auctions with incomplete information. There are two symmetric players whose values can be high or low, which are their private information. The contest organizer observes the players’ values ex post, and she can commit ex ante to four different symmetric information policies exhaustively. First, she can always disclose publicly the types of the players regardless. Second, she can conceal the types of the players regardless. Third, she can disclose publicly the players’ types if and only both are of high type. Fourth, she can disclose publicly the players’ types if and only both are of low type. We characterize explicitly the unique equilibrium for every scenario. Based on the equilibrium analysis, we are able to completely rank the four disclosure policies by the expected effort induced and players’ expected payoffs. We find that the full concealment policy extracts the highest aggregate expected efforts, which is followed by the policy of disclosing types if and only if both are high, and the policy of disclosing types if and only if both are low induces the least total expected effort. The players enjoy the highest expected payoffs under the policy of disclosing types when both are low, and all other three policies render the same expected payoffs to the players.
JEL Classifications
  • C7 - Game Theory and Bargaining Theory
  • D4 - Market Structure, Pricing, and Design