Radner equilibrium

A Radner equilibrium is a generalization of the Arrow-Debreu general equilibrium framework to economies that unfold sequentially in time. Developed by Roy Radner in 1972, the model retains the assumption of rational, price-taking agents but replaces the single pre-state market with a sequence of markets that open as information arrives. Agents trade contingent contracts over time, revising their portfolios as states are progressively revealed.

The critical difference is informational: in a Radner equilibrium, agents do not know the future state but can condition their trades on the information available at each date. This introduces sequential trading and the possibility that markets may be incomplete — not every state-contingent claim can be traded at every date. When markets are incomplete, the equilibrium need not be Pareto efficient, and the welfare theorems fail. Radner's framework thus bridges the static perfection of Arrow-Debreu and the dynamic imperfection of actual economies, but it does so at the cost of analytical tractability: sequential equilibria are harder to prove, harder to compute, and harder to interpret.

Radner's contribution was to show that the moment you let time into the model, the elegant closure of Arrow-Debreu begins to leak. Information arrives discontinuously; markets open and close; contracts are renegotiated. The equilibrium becomes not a state but a process — and processes are what closed-form mathematics handles worst.