SGMR co-evolves strategies and multilayer economic links under one dynamic potential, converging faster with higher welfare and stronger noise resilience on synthetic networks
This paper develops a co-evolutionary multilayer potential game in which boundedly rational agents update mixed strategies while market, information, and institutional links adapt to observed compatibility and diffusion signals, and proposes a stability-guarded mirror-replicator (SGMR) dynamic combining entropy-regularized strategy revision, projected link rewiring, and a spectral safeguard; the authors prove that the mirror step recovers replicator dynamics in the small-step limit and establish the exact-potential property, monotone potential improvement, sublinear stationarity, and local input-to-state stability under observation disturbances, with computational experiments on synthetic economic networks showing faster convergence, higher collective welfare, stronger noise resilience, an