Defection-Free Collaboration between Competitors in a Learning System

TL;DR

This work analyzes collaboration between competing model-training firms as a duopoly, showing that naive full collaboration collapses revenues while partial sharing can help. It develops Defection-Free Collaborative Learning (Defection-Free CL), an algorithm that guarantees non-decreasing revenues for both firms and converges to the Nash bargaining solution $(q_l^*,q_h^*)$, with $q_h^* = \max_x q(x)$. The approach relies on a coordinated sharing protocol and paced updates to avoid revenue loss, and it provides theoretical convergence guarantees and rates. Empirical validation on MNIST demonstrates revenue growth and convergence toward the Nash point, suggesting a practical path to defect-free collaboration in data-sharing settings with complementary data distributions.

Abstract

We study collaborative learning systems in which the participants are competitors who will defect from the system if they lose revenue by collaborating. As such, we frame the system as a duopoly of competitive firms who are each engaged in training machine-learning models and selling their predictions to a market of consumers. We first examine a fully collaborative scheme in which both firms share their models with each other and show that this leads to a market collapse with the revenues of both firms going to zero. We next show that one-sided collaboration in which only the firm with the lower-quality model shares improves the revenue of both firms. Finally, we propose a more equitable, *defection-free* scheme in which both firms share with each other while losing no revenue, and we show that our algorithm converges to the Nash bargaining solution.

Figures (8)

• Figure 1: Performance of Complete Sharing scheme on MNIST. When both firms share with each other, their models converge to the same utility, driving their utilities to zero.
• Figure 2: Performance of One-sided Sharing schemes on MNIST. When only the high-quality firm shares, the high-quality firm's revenue becomes negative. When only the low-quality firm shares, both firms have positive, but less, revenue than with our collaboration scheme (Figure \ref{['fig:nash sharing utilities']}).
• Figure 3: Performance of Defection-Free FL on MNIST. Both firms' qualities increase (figure 1), their revenues increase and approach a higher level than under One-sided Collaboration (figure 2), and the firms' qualities approach the Nash bargaining solution (figure 4).
• Figure 4: This figure shows how the firms' utilities vary with model quality. $U_l$ and $U_h$ are both increasing in $q_h$, $U_h$ is decreasing in $q_l$, and $U_l$ is increasing in $q_l$ for $q_l \leq \frac{4q_h}{7}$ and decreasing in $q_l$ otherwise.
• Figure 5: $B(a,b) \geq a$ for all $b \geq 1$.

Theorems & Definitions (31)

• Definition 1
• Lemma 1: Consumer Demands
• proof
• Definition 2
• Lemma 2: Equilibrium Prices and Utilities
• proof
• Proposition 2.1: Relationship between utilities and qualities
• proof
• Lemma 3: Firm revenues under Complete Collaboration
• Proposition 4.1: Equivalence between maximal quality and the Nash bargaining solution