Dynamic discrete choice under rational inattention

Geometric methods for finite rational inattention

“…Although our approach is static in nature, it can easily be incorporated into iterative algorithms that account for these dynamic incentives, such as the one proposed by Miao and Xing (2023) for situations with unobservable payoffs. They express the agent's problem at any history as a static problem with payoffs given by appropriately constructed value vectors, then approximate the agent's optimal learning strategy using an iteration of the Blahut-Arimoto algorithm, and in turn use these strategies to update the associated (Markovian) beliefs and continuation values.…”

“…We use this well-known application to benchmark the GAP-SQP algorithm described in Section 4.3 against existing methods, focusing primarily on speed. We then extend this model to multiple interconnected periods to highlight how our algorithm can be combined with the iterative approach of Miao and Xing (2023) to tackle dynamic RI problems. The second is a portfolio choice problem with a massive state and action space proposed by Jung et al (2019).…”

“…We discretize the action and state spaces with 100 and 300 grid points, respectively, and consider a time horizon of T = 10 periods, resulting in 901 interconnected RI problems. 15 We implement the iterative algorithm suggested by Miao and Xing (2023) using either the Blahut-Arimoto or the GAP-SQP subroutine to update strategies. Figure 6(a) plots the welfare that is achieved by the algorithmic solutions after different running times.…”

“…We plot the maximal score s across all actions in any subgame, knowing that it should be zero under the optimal choice. It takes 14 As in Miao and Xing (2023), we assume that the agent cannot learn "for free" simply by observing past payoff realizations. 15 The full solution specifies the agent's initial choice, as well as her continuation strategy after each of 100 Markov histories p t−1 during each of the subsequent time periods.…”

“…We document that our algorithm is orders of magnitude faster than the wellknown Blahut-Arimoto algorithm (see Cover and Thomas (2012)) and scales well with the size of the action and state spaces. The superior convergence speed is maintained when the algorithm is integrated in dynamic algorithms such as the one suggested by Miao and Xing (2023). Precision, rather than speed, is the focus of our second application, based on the two-dimensional portfolio design problem of Jung, Kim, Matějka, and Sims (2019).…”