In standard evolutionary game theory, defectors beat cooperators because defection pays more per interaction. Cooperators persist only through spatial clustering, kin selection, or repeated-game reciprocity. The mechanisms are well-studied but fragile — they work in models, less reliably in messy populations.
Wang et al. (arXiv:2603.10488) add one ingredient: interaction payoffs scale with the minimum wealth of the participants. Two rich cooperators playing together get a large payoff. A rich cooperator playing a poor defector gets a small payoff, scaled down by the defector's poverty. The defector's short-term gain from defection is real but self-limiting — each defection impoverishes the defector, which shrinks future payoffs from all interactions.
The dynamics produce a discontinuous transition. At the boundary between cooperator and defector regions on a lattice, a wealth gradient builds up. Cooperators on one side have accumulated resources; defectors on the other have depleted theirs. As the gradient sharpens, boundary movement slows — because cross-boundary interactions produce tiny payoffs (scaled by the poor side's wealth). The boundary stalls. The stalling triggers an explosive gradient buildup that locks the boundary in place.
The result: cooperators dominate not by outcompeting defectors in individual interactions but by building a wealth wall that defectors can't cross. The wall is self-reinforcing — the richer cooperators get, the less they lose from boundary interactions, and the poorer the defectors get, the less they gain from any interaction at all.
The counterintuitive finding: thermal noise (random strategy switching) strengthens cooperation rather than weakening it. In most cooperation models, noise helps defectors invade cooperative clusters. Here, noise occasionally converts a boundary defector to cooperation, which instantly gives them access to the cooperator side's wealth pool — a jump that's irreversible because switching back to defection means leaving the pool. The noise is asymmetric: cooperator-to-defector transitions are temporary (you quickly impoverish); defector-to-cooperator transitions are sticky (you quickly enrich).