Inducing Efficient and Equitable Professional Networks through Link Recommendations

TL;DR

The paper addresses how two-group dynamics in professional networks shape labor-market inequality and how platform link recommendations influence outcomes. It develops a theoretical model with exogenous and endogenous opportunities, where a platform subsidizes connections and can promote cross-group links; equilibria are analyzed under a defection-free pairwise Nash concept. A key finding is that facially neutral platforms can increase inequality when exogenous disparity is large, while cross-group link recommendations reduce inequality and raise welfare (utilitarian and Rawlsian) across equilibria. The results highlight that integrating platforms—through thoughtful cross-group subsidies—can align platform utility with broader societal equity and efficiency, informing design and regulation of professional networking systems. The work also outlines rich directions for future research, including more than two groups, heterogeneous opportunities, and noisy information regimes.

Abstract

Professional networks are a key determinant of individuals' labor market outcomes. They may also play a role in either exacerbating or ameliorating inequality of opportunity across demographic groups. In a theoretical model of professional network formation, we show that inequality can increase even without exogenous in-group preferences, confirming and complementing existing theoretical literature. Increased inequality emerges from the differential leverage privileged and unprivileged individuals have in forming connections due to their asymmetric ex ante prospects. This is a formalization of a source of inequality in the labor market which has not been previously explored. We next show how inequality-aware platforms may reduce inequality by subsidizing connections, through link recommendations that reduce costs, between privileged and unprivileged individuals. Indeed, mixed-privilege connections turn out to be welfare improving, over all possible equilibria, compared to not recommending links or recommending some smaller fraction of cross-group links. Taken together, these two findings reveal a stark reality: professional networking platforms that fail to foster integration in the link formation process risk reducing the platform's utility to its users and exacerbating existing labor market inequality.

Figures (4)

• Figure 1: For large enough exogenous utility ratio, a network without link recommendations increases inequality, relative to exogenous levels. In the plot above, for each line, we fixed $g$ and vary $b$ plotting the value of $\mathsf{UR}(\varnothing) = (1-g_0)/(1-b_0)$ on the horizontal axis. On the vertical axis, we plot upper bounds (in red) and lower bounds (in blue) for the utility ratio $(\mathsf{UR}(E), E \in \mathcal{E})$ achieved for all equilibria at these parameter values. We set $\gamma = 0.04$.
• Figure 2: For large enough exogenous utility ratio, cross-group link recommendations reduce inequality, relative to exogenous levels. In the plot above, for each line, we fix $g$ and vary $b$, plotting the value of $\mathsf{UR}(\varnothing) = (1-g_0)/(1-b_0)$ on the horizontal axis. On the vertical axis, we plot upper bounds for the utility ratio ($\mathsf{UR}(E)$, $E \in \mathcal{E}$) achieved for all equilibria at these parameter values. We set $\gamma = 0.04$, $k=1$ and $\rho = 1$.
• Figure 3: We plot average utility against the number of cross-group recommendations made. It is always better to make $k > 0$ cross-group recommendations than to not make any recommendations. We set $b_0$ so that the exogenous utility ratio is always $2$. We set $\gamma = 0.02$ and $\rho = 1$.
• Figure 4: We plot upper (in red) and lower bounds (in blue) on average utility $n^{-1} \sum_{i=1}^n u_i(E)$ minus exogenous utility ($\sum_{i=1}^n(1 - p_{i0})$) against the fraction of cross-group link recommendations $\rho$, keeping $k=5$ constant. We set $b_0$ so that the exogenous utility ratio is always $2$. We set $\gamma = 0.02$.

Theorems & Definitions (19)

• Lemma 3.1
• Proposition 4.1
• proof
• Proposition 4.2
• Corollary 4.3
• Proposition 5.1
• Proposition 5.2
• Lemma B.1
• proof : Proof of \ref{['lem:no-blue-edges']}
• Lemma B.2