Rational Inattention via Ignorance Equivalence

A previous version of this working paper was published in September 2021, which, along with Working Paper 21-30, superseded Working Paper 20-24 – Rational Attention via Ignorance Equivalence

We introduce the concept of the ignorance equivalent to effectively summarize the payoff possibilities of an agent who is facing a finite Rational Inattention (RI) problem. The ignorance equivalent is a unique fictitious action that does not distort learning incentives when added to the agent’s menu but also makes ignorance optimal. In doing so, it allows us to restate the RI problem as a choice over a richer menu without learning. The approach provides new insights for menu expansion, the formation of consideration sets, the trading of information, and belief elicitation. We fully characterize the relationship between the ignorance equivalent and the optimal choice in the original RI problem. When multiple RI agents with different learning costs interact, the ignorance equivalent emerges in equilibrium, facilitating trade that allows agents to emulate the first-best learning strategy.