Hiring under Congestion and Algorithmic Monoculture: Value of Strategic Behavior

TL;DR

We study hiring from a shared applicant pool when multiple firms use a common scoring algorithm, creating congestion and algorithmic monoculture. The paper develops a threshold-based Nash equilibrium characterization under two offer-correlation regimes, and compares Naive, NE, and Centralized benchmarks to quantify welfare via PoNS and PoA. Key findings show NE can substantially improve social welfare over Naive, with PoNS large in low-capacity/high-firm regimes and PoA approaching 1, while convergence to NE is possible with simple best-response dynamics and per-applicant competition information. The results have practical implications for platform design, suggesting congestion signaling and personalization can facilitate efficient outcomes for firms and applicants in algorithmic hiring markets.

Abstract

We study the impact of strategic behavior in a setting where firms compete to hire from a shared pool of applicants, and firms use a common algorithm to evaluate them. Each applicant is associated with a scalar score that is observed by all firms, provided by the algorithm. Firms simultaneously make interview decisions, where the number of interviews is capacity-constrained. Job offers are given to those who pass the interview, and an applicant who receives multiple offers accepts one of them uniformly at random. We fully characterize the set of Nash equilibria under this model. Defining social welfare as the total number of applicants who find a job, we then compare the social welfare at a Nash equilibrium to a naive baseline where all firms interview applicants with the highest scores. We show that the Nash equilibrium greatly improves upon social welfare compared to the naive baseline, especially when the interview capacity is small and the number of firms is large. We also show that the price of anarchy is small, providing further appeal for the equilibrium solution. We then study how the firms may converge to a Nash equilibrium. We show that when firms make interview decisions sequentially and each firm takes the best response action assuming they are the last to act, this process converges to an equilibrium when interview capacities are small. However, we show that the task of computing the best response is difficult if firms have to use its own historical samples to estimate it, while this task becomes trivial if firms have information on the degree of competition for each applicant. Therefore, converging to an equilibrium can be greatly facilitated if firms have information on the level of competition for each applicant.

Figures (5)

• Figure 1: Plots of the utility curves $U_n(s)$ when $\theta \in \{\textsc{Corr}, \textsc{Indep}\}$ and $n = 1, \dots, 6$.
• Figure 2: Examples of equal-utility equilibria when $N = 2$ and $\theta = \textsc{Corr}$. An equilibrium is characterized by the dashed red horizontal line in the upper plots. The lower plots depict two possible strategy profiles that form an NE with the corresponding thresholds. In Figure \ref{['fig:ex1']}, $c=0.2$ and the equilibrium is characterized by the horizontal line $y=0.6$ with $\tau_1 = 0.6$. In Figure \ref{['fig:ex2']}, the capacity is $c = 0.35$ and an equal-utility equilibrium is characterized by $y=13/30$ with $\tau_1 = 13/30$ and $\tau_2 = 13/15$.
• Figure 3: Example of a variable-utility equilibrium with $N = 2$, $\theta = \textsc{Corr}$, and $c = 0.35$. $f_A(s) = 1$ if and only if $s\in[0.4, 0.55]\cup [0.8,1]$, and $f_B(s) = 1$ if and only if $s\in[0.55, 0.8]\cup [0.9,1]$. The dashed horizontal lines highlight the utility at the two thresholds $\tau_1$ and $\tau_2$. Under this strategy profile, $\tau_1 = 0.4$ and $\tau_2 = 0.9$, and the utility at the thresholds are $U_1(\tau_1) = 0.4$ and $U_2(\tau_2) = 0.45$.
• Figure 4: Comparison of utility curves $U_n(s)$ and the thresholds for $n \in \{1, 2, \dots, 6\}$ under $\theta = \{\textsc{Corr}, \textsc{Indep}\}$. The dashed horizontal line $y=0.2$ characterizes equal-utility equilibria. When $\theta = \textsc{Corr}$, the thresholds are evenly spaced across the applicant score $s$. In contrast, when $\theta = \textsc{Indep}$, most thresholds are concentrated near $s = 0$; hence a large portion of applicants who receive interviews will be interviewed by the same number of firms.
• Figure 5: For $p_1 \in \{0.1, 0.5\}$, $p_2 > p_1$, and $q \in \{0.8, 0.9, 0.95\}$, we compute the smallest number of samples $k$ needed so that if $X_1 \sim \text{Binom}(k, p_1)$ and $X_2 \sim \text{Binom}(k, p_2)$, then $\mathbb{P}(X_1 < X_2) \geq q$. We vary $p_2$ from $p_1 + 0.05$ to $p_1+0.3$ in increments of 0.01.

Theorems & Definitions (45)

• Theorem 3.1
• Definition 3.1
• Proposition 3.1
• Proposition 3.2
• Theorem 4.1
• Theorem 4.2
• Theorem 4.3
• Theorem 4.4
• Theorem 4.5
• Theorem 5.1