We describe conditions for the existence of a stationary Markovian equilibrium when total production or total endowment is a random variable. Apart from regularity assumptions, there are two crucial conditions: (i) low information — agents are ignorant of both total endowment and their own endowments when they make decisions in a given period, and (ii) proportional endowments — the endowment of each agent is in proportion, possibly a random proportion, to the total endowment. When these conditions hold, there is a stationary equilibrium. When they do not hold, such equilibrium need not exist.
Karatzas, Ioannis; Shubik, Martin; and Sudderth, William D., "Information and the Existence of Stationary Markovian Equilibrium" (2000). Cowles Foundation Discussion Papers. 1512.