Evolutionary dynamics of adaptive multilayer economic networks: a stability-guarded potential game framework

Abstract

Complex economic and social systems emerge from repeated strategic interactions on networks whose links also change with behavior. Existing evolutionary-game models commonly assume fixed-interaction structures, whereas adaptive-network approaches often lack a global incentive certificate and an explicit stability condition. 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. We propose a stability-guarded mirror-replicator (SGMR) dynamic that combines entropy-regularized strategy revision, projected link rewiring, and a spectral safeguard. The mirror step is shown to recover replicator dynamics in the small-step limit. We prove the exact-potential property, monotone potential improvement, sublinear stationarity, and local input-to-state stability under observation disturbances. Computational experiments on synthetic economic networks show faster convergence, higher collective welfare, stronger resilience to noise, and more stable network adaptation than static mirror ascent, standard replicator dynamics, and fictitious play. Additional diagnostics directly evaluate the input-to-state stability bound, quantify the empirical residual decay, and confirm statistically significant welfare gains across network topologies. This framework links evolutionary dynamics, adaptive multilayer networks, and decentralized collective decision-making in complex social systems.