Balancing Selection Efficiency and Societal Costs in Selective Contests

TL;DR

This paper models the trade-off between selection efficiency and societal costs in contests, showing that introducing randomness can optimize societal welfare without sacrificing efficiency.

Contribution

It characterizes the feasible set of efficiency and societal costs in contest design and proposes a method to optimize linear payoffs through randomness.

Findings

Selection efficiency and welfare are generally inversely related.

Introducing randomness can improve societal costs without reducing efficiency.

Optimal contest design involves adjusting a single parameter related to randomness.

Abstract

Selective contests can impair participants' overall welfare in overcompetitive environments, such as school admissions. This paper models the situation as an optimal contest design problem with binary actions, treating effort costs as societal costs incurred to achieve a desired level of selectivity. We provide a characterization for the feasible set of selection efficiency and societal cost in selective contests by establishing their relationship with feasible equilibrium strategies. We find that selection efficiency and contestants' welfare are complementary, i.e. it is almost impossible to improve one without sacrificing the other. We derive the optimal equilibrium outcome given the feasible set and characterize the corresponding optimal contest design. Our analysis demonstrates that it is always optimal for a contest designer who is sufficiently concerned with societal cost to intentionally introduce randomness into the contest. Furthermore, we show that the designer can optimize any linear payoff function by adjusting a single parameter related to the intensity of randomness, without altering the specific structure of the contest.