Using a rigorous convergence probability, this note shows why mathematic models are inconsistent with empirical evidence. Using a dynamic quadratic cointegration, a new theory of the concave utility shows that below the optimum, the volatility has a positive impact upon output. Beyond the optimum, the volatility of policy has a negative impact upon output and a positive impact upon the unemployment rate. In this new methodology, our equilibrium targets minimize inflation bias and fiscal bias. First, we compute the equilibrium and optimal policy, then reduce the heteroschedasticity, and finally estimate the convergence probability. Our surprising solution is individually rational and feasible while the budget is balanced over business cycles. For the problem of n>1 governments or agents, an agent estimates and proposes the maximum non-zero equilibrium which is most acceptable to all participants and outperforms the Nash noncooperative equilibrium. This solves the games and scientific problems unrelated to games as n→∞, regardless of whether the proposal is accepted voluntarily or not.