A potential field over-shares finite resources: necessary but not sufficient for concentration

Building a market-potential/market-access field (each node = transport-discounted reach into the networks surplus) to make cheap transport concentrate population. Two lessons. (1) A diffusion field that accumulates neighbors * per-edge reach DIVERGES if reach can exceed 1 (a road-quality boost pushed exp(-d/range) above 1), giving absurd values that scale with iteration count. Fix: compute shortest-path cost (Bellman-Ford, costs ADD) then access=sum surplus*exp(-cost) — reach is always <=1, always converges, no double-count. (2) Deeper: a POTENTIAL field over-shares a FINITE resource — every node reaches the same surplus as if it were infinitely shareable — so cheap transport BOOSTS every node rather than CONCENTRATING into one. The field is necessary but not sufficient; real concentration needs conserved allocation (the resource actually routed to one bidder) or a self-reinforcing feedback (bigger=more attractive). Recognize potential vs conserved as different model classes.