Market selection and learning under model misspecification

Market structure or agent rationality: How efficiency trades with belief updating?

“…Hence, similarly to the case investigated in Bottazzi et al (2023), agents' beliefs show a Markov structure. Invoking the Strong Law of Large Numbers, for any agent i one obtains, almost surely,…”

“…Equation ( 11), together with equation ( 10), perfectly resembles one of the standard ways of representing the Bayesian learning process (see Massari, 2017Massari, , 2020Marinacci and Massari, 2019;Bottazzi et al, 2023). Thus, following the procedure used by Massari (2020) and Bottazzi et al (2023), call Π n t = max i∈{1,...,N } Π i,n t and j n,t one of the agents such that Π jn,t,n t = Π n t , in this way one has…”

“…In line with the literature on Bayesian learning (see e.g. Epstein et al, 2010;Beygelzimer et al, 2012;Massari, 2020;Bottazzi et al, 2023), we assume that agents build their probabilistic predictions for the occurrence of the event at time t as a weighted average of the probabilities suggested by the two models, that is…”

“…Taking the limit for t → ∞ and invoking Lemma A.1 of Bottazzi et al (2023), under the assumption that the limits involved exist, one almost surely obtains 2 0 = lim…”

“…While agents follow the same investment behavior, they have heterogeneous beliefs that are generated by means of a learning process over two misspecified models, one optimist and one pessimist, that are agent-specific. In our framework model misspecification represents the complexity of the environment in which agents operate: it captures the fact that in a complex world the models agents have in mind are simplistic representations of the true data generating process (Bottazzi et al, 2023). We assume that the learning protocol of each agent depends on the number n of previous data points (i.e.…”