Do Sunspots Matter under Complete Ignorance?

In a two-period, sunspot, pure-exchange economy we analyze the case in which agents do not assign subjective probabilistic beliefs to the `sunspot activity'. Two generations, each of which is made up of identical agents, populate this economy. The participation in the Arrow securities market is restricted and the generation, which is allowed to trade in assets, can alternatively face uncertainty via two distribution-free decision rules under `complete ignorance' (axiomatized by Milnor (1954)): the `minimax regret criterion' (Savage (1954), ch.9) and the `maxmin return criterion' (Wald (1950)). When the former is used, then sunspots can matter. In particular we prove that, if the economy admits two Walrasian equilibria, then a unique sunspot equilibrium always exists. We pin down this equilibrium, determine the prices of the Arrow securities and show that, at these prices, no trade in securities takes place. In the same framework we prove that, with agents using the maxmin return criterion, sunspots do not matter.