Measuring the informativeness of economic actions and market prices

In many circumstances economic agents are partially ignorant about payo↵-relevant state variables, but must nonetheless decide what action to take. To give just one example, investment decisions must often be made without full knowledge of the rate of return. In many such cases, agents can potentially obtain useful information by observing either the actions of other agents, or market prices. However, the information content of such actions or prices is in general hard to order, outside of special cases in which linearity arises. This paper deploys Lehmann’s (1988) information ordering to this class of problems. First, I relate Lehmann’s ordering to supermodularity properties. Second, I obtain a tractable first-order version of Lehmann’s ordering. Third, I relate this first-order condition to both individual optimization problems and to equilibrium pricing conditions.