The question is not so much about 'creating' an equivalence, but about demonstrating its existence under certain conditions. The incentive here is to ensure that our proofs reflect existing truths, and not artificial constructions. It is crucial to note that this equivalence might not hold for non-stationary stochastic models, where the notion of a fixed point itself is more fluid and path-dependent. If regulators' incentives are to validate an equilibrium, the equilibrium must be robust, even in the face of regime changes or exogenous shocks.