Economic Security of Multiple Shared Security Protocols

As restaking protocols gain adoption across blockchain ecosystems, there is a need for Actively Validated Services (AVSs) to span multiple Shared Security Providers (SSPs). This leads to stake fragmentation which introduces new complications where an adversary may compromise an AVS by targeting its weakest SSP. In this paper, we formalize the Multiple SSP Problem and analyze two architectures : an isolated fragmented model called Model $\mathbb{M}$ and a shared unified model called Model $\mathbb{S}$, through a convex optimization and game-theoretic lens. We derive utility bounds, attack cost conditions, and market equilibrium that describes protocol security for both models. Our results show that while Model $\mathbb{M}$ offers deployment flexibility, it inherits lowest-cost attack vulnerabilities, whereas Model $\mathbb{S}$ achieves tighter security guarantees through single validator sets and aggregated slashing logic. We conclude with future directions of work including an incentive-compatible stake rebalancing allocation in restaking ecosystems.