Rational Inattention via Ignorance Equivalence

Geometric methods for finite rational inattention

“…where (j|i) denotes the exogenously given probability that the state transitions from i to j, β is the discount factor, and α t+1 j (a t ) denotes the ignorance equivalent of the continuation problem that ensues under the posteriors associated with action a t . The ignorance equivalent in turn is determined from the choice probabilities in the subsequent periods, dating back to Caplin, Dean, and Leahy (2018) and generalized in Müller-Itten, Armenter, and Stangebye (2023),…”

“…The payoffs from the preimage describe a fictitious action that, whether added to the original menu or offered in replacement of it, leaves the decision‐maker no better or worse off. It is precisely the ignorance equivalent of the RI problem, as defined in Müller‐Itten, Armenter, and Stangebye (2023), and can play a strategic role in contract games with RI agents.…”

“…Learning generates payoff complementarities across actions (Müller‐Itten, Armenter, and Stangebye (2023)). When using discrete approximations to continuous problems, it is thus possible that even a fine grid over actions and states fails to capture the full learning opportunities, and that any approximation thus dismisses some actions in error.…”

“…We can compute the ignorance equivalent of this RI investment problem, obtained as the preimage of the optimal attention vector. This fictitious asset is uniquely designed to ensure that the investor would abandon learning and select it unconditionally, but without gaining a payoff boost in doing so (Müller‐Itten, Armenter, and Stangebye (2023)). The ignorance equivalent yields the same expected utility as the optimal portfolio choice with learning, but—as can be seen from the payoff distribution in Figure 8—it avoids the lowest payoffs to dissuade learning.…”