Joint survival under resource pooling with load-dependent returns

For geometric Brownian resources with drift $\mu$ and volatility $\sigma$, continuous equalisation within a group of size $k$ raises the drift of log resources from $\mu-\sigma^2/2$ to $\mu-\sigma^2/(2k)$. We consider a fixed set of $N$ agents whose common drift $\mu(n)$ depends on the number $n$ of agents not yet ruined, partitioned into fixed pooling groups, with an absorbing floor. For every fixed partition, the probability that no agent is ever ruined equals $\prod_jp_{k_j}(\mu(N))$, an explicit product over groups, and the probability of no ruin by a finite time has the corresponding closed form. Consequently, the probability that all agents avoid ruin is positive under complete pooling exactly when $N\mu(N)>\sigma^2/2$; complete pooling is then strictly the best fixed partition, and otherwise no fixed partition gives a positive probability. If any agents survive forever, their number lies almost surely in the material viability set $\{n:\ n\mu(n)>\sigma^2/2\}$; in the linear example this set is either empty or consists of the integers in a bounded viability window. Combined with an information model in which surviving agents learn from one another's products, joint material--information persistence of all agents additionally requires $(N-1)\nu R\ge\eta$, and any persistence at all requires a terminal population size in the viability set that also satisfies the information condition. Monte Carlo simulations agree with the exact finite-horizon probabilities. The results distinguish all-agent survival, determined by the return at the initial load, from terminal viability, determined by the return at the surviving load.