In an infinite-time decentralized sequence economy, agents use fiat money to bridge markets as if they make trades in a centralized economy, to avoid huge transaction cost that all agents’ going together must incur. The model in this paper formulates the process how agents decide the fiat money’s nominal value. Three new concepts are suggested – plan of choices, Temporarily Partial Equilibrium and Intra-Date Equilibrium; and this paper proves the existence of these two equilibriums. Then, based on the equilibrium prices and allocations of the corresponding infinite-time Walrasian economy, this paper proves that all agents’ accepting fiat money with unchanged nominal value is a Nash equilibrium, which guarantees fiat money’s essentiality.
