Gradient Swapping for Effective Agent Reconfiguration?

We study a distributed ensemble where each agent holds a goal cell on a shared grid, maintains a local hop estimate toward free anchors, repairs duplicate assignments, and occasionally proposes a pairwise goal swap when both sides reduce Manhattan cost. The question in the title is intentional: when does greedy swapping plus gradient gossip actually reconfigure the team into a target layout without central planning?

This note pairs the algorithm sketch with a lightweight simulator. The toy matches our desktop pygame prototype: same communication radius, move cooldown, duplicate-goal resolution, and mutual swap acceptance rule.

Initial observations: when the grid is sparse and goal assignments are close to each other, swapping converges faster than random reassignment. When density exceeds ~60% occupancy, deadlock probability rises sharply and a backoff rule is needed. More runs pending.

The formal bound on convergence time under greedy swapping is an open problem. We conjecture it is polynomial in team size for sparse grids, but have no proof yet. If you work on multi-agent path finding and have thoughts, reach out.