Platforms for Efficient and Incentive-Aware Collaboration

TL;DR

This work proposes a framework where the platform has more information about how the agents' tasks relate to each other than the agents themselves, and describes how and to what degree such platforms can leverage their information advantage to steer strategic agents toward efficient collaboration.

Abstract

Collaboration is crucial for reaching collective goals. However, its effectiveness is often undermined by the strategic behavior of individual agents -- a fact that is captured by a high Price of Stability (PoS) in recent literature [Blum et al., 2021]. Implicit in the traditional PoS analysis is the assumption that agents have full knowledge of how their tasks relate to one another. We offer a new perspective on bringing about efficient collaboration among strategic agents using information design. Inspired by the growing importance of collaboration in machine learning (such as platforms for collaborative federated learning and data cooperatives), we propose a framework where the platform has more information about how the agents' tasks relate to each other than the agents themselves. We characterize how and to what degree such platforms can leverage their information advantage to steer strategic agents toward efficient collaboration. Concretely, we consider collaboration networks where each node is a task type held by one agent, and each task benefits from contributions made in their inclusive neighborhood of tasks. This network structure is known to the agents and the platform, but only the platform knows each agent's real location -- from the agents' perspective, their location is determined by a random permutation. We employ private Bayesian persuasion and design two families of persuasive signaling schemes that the platform can use to ensure a small total workload when agents follow the signal. The first family aims to achieve the minmax optimal approximation ratio compared to the optimal collaboration, which is shown to be $Θ(\sqrt{n})$ for unit-weight graphs, $Θ(n^{2/3})$ for graphs with constant minimum edge weights, and $O(n^{3/4})$ for general weighted graphs. The second family ensures per-instance strict improvement compared to full information disclosure.

Figures (5)

• Figure 1: Double Star Graph. Formally, let $\theta_v$ denote the contribution of node $v$. The social optimum is achieved when $\theta_{x_0}=\theta_{y_0}=1$ with all other $\theta_v=0$. Feasibility requires that each agent $v$ receives a total contribution of $\theta_v + \sum_{u: \{u,v\}\in E} \theta_u \geq 1$. Stability requires no node can unilaterally reduce their contribution without hurting their own feasibility. Following are typical stable solutions: (1) One-sided leaf contribution, where $\theta_v=1$ for $v\in\{x_1, x_2, \ldots, x_k, y_0\}$ and $\theta_v=0$ for the rest, and (2) Full leaf contribution, with $\theta_v=1$ for all leaf nodes $v\in\{x_1, x_2, \ldots, x_k, y_1, y_2, \ldots, y_k\}$, while $\theta_{x_0}=\theta_{y_0}=0$. Both solutions suffer from a total workload of $\Omega(k)$.
• Figure 2: Plan A (left) and Plan B (right) for the double-star graph. The shaded vertices are labeled with $1 - \epsilon$. The empty vertices are labeled with $0$.
• Figure 3: $\mathsf{Cut}({\mathsf{IS}},V\setminus {\mathsf{IS}})$. Every vertex in ${\mathsf{IS}}$ has a neighbor in ${\mathsf{DS}}$; every vertex in $V \setminus ({\mathsf{DS}} \cup {\mathsf{IS}})$ has a neighbor in ${\mathsf{IS}}$.
• Figure 4: A weighted graph on which all binary schemes fail. There are $k$ triangles in total. Each thick line indicates the edges between a center and all the three vertices in a triangle. Every edge is of weight $1/2$.
• Figure 5: The three plans (left: Plan A; middle: Plan B; right: Plan C) of signaling for the graph from \ref{['fig:binary-schemes-fail']}. Shaded circle vertices are labeled with $1 - \epsilon$. Empty circle vertices are labeled with $0$. Shaded square vertices are labeled with $\alpha$.

Theorems & Definitions (50)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Theorem 1.4
• Lemma 2.1: Identity-independent signaling schemes
• Definition 3.1: Slack
• Lemma 3.2: Persuasiveness of general signaling schemes
• proof : Proof sketch
• Definition 3.3: Weights of Cut and Induced Subgraph
• Lemma 3.4: Persuasiveness of binary signaling schemes