A Rigorous Mathematical Framework for Multi-Agent Flexible Consensus Investment Systems

This paper develops a rigorous mathematical framework for a multi-agent adaptive investment ecosystem, addressing five critical gaps in the existing literature. Relative to the prior version, we introduce three substantial improvements. First, we resolvethe identification problem in the evolutionarily stable strategy (ESS) by replacing unobservable true-state precision with a proxy precision estimator based on ex-post realized returns, making the ESS empirically testable. Second, wereplace the static Bayesian game with an asynchronous dynamic Bayesian game, unifying the temporal logic of the consensus mechanism and portfolio choice problem and providing a tighter convergence guarantee via asynchronous contraction mapping theory.Third, we relax the strong-connectivity assumption to joint strong connectivity, aligning the theoretical framework with sparse, hub-dominated financial networks.We additionally establish a potential-game representation that yields BNEuniqueness without imposing large risk-aversion requirements. Monte Carlo simulations under four market regimes confirm our theoretical results; an empirical validation design using Chinese mutual fund data and a DeFi liquidation dataset providesout-of-sample evidence.