arXiv subjects
Publications and source records attributed to Ignacio Esponda.
This chapter develops a unified framework for studying misspecified learning situations in which agents optimize and update beliefs within an incorrect model of their environment. We review the statistical foundations of learning from misspecified models and extend these insights to environments with endogenous, action-dependent data, including both single agent and strategic settings.
We study learning in complete-information games, allowing the players' models of their environment to be misspecified. We introduce Berk--Nash rationalizability: the largest self-justified set of actions -- meaning each action in the set is optimal under some belief that is a best fit to outcomes generated by joint play within the set. We show that, in a model where players learn from past actions, every action played (or approached) infinitely often lies in this set. When players have a correct model of their environment, Berk--Nash rationalizability refines (correlated) rationalizability and coincides with it in two-player games. The concept delivers predictions on long-run behavior regardless of whether actions converge or not, thereby providing a practical alternative to proving convergence or solving complex stochastic learning dynamics. For example, if the rationalizable set is a singleton, actions converge almost surely.
We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This framework has become increasingly popular in economics to study behavior driven by incorrect or biased beliefs. Current literature has characterized asymptotic behavior under fairly specific assumptions. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a generalization of a differential equation that describes the evolution of the frequency of actions. We then present a series of implications that can be readily applied to economic applications, thus providing off-the-shelf tools that can be used to characterize behavior under misspecified learning.
In developing the theory of long-run competitive equilibrium (LRCE), Marshall (1890) used the notion of a representative firm. The identity of this firm, however, remained unclear. Subsequent theory either focused on the case where all firms are identical or else incorporated heterogeneity but disregarded the notion of a representative firm. Using Hopenhayn's (1992) model of competitive industry dynamics, we extend the theory of LRCE to account for heterogeneous firms and show that the long-run supply function can indeed be characterized as the solution to the minimization of a representative average cost function.
We study Markov decision problems where the agent does not know the transition probability function mapping current states and actions to future states. The agent has a prior belief over a set of possible transition functions and updates beliefs using Bayes' rule. We allow her to be misspecified in the sense that the true transition probability function is not in the support of her prior. This problem is relevant in many economic settings but is usually not amenable to analysis by the researcher. We make the problem tractable by studying asymptotic behavior. We propose an equilibrium notion and provide conditions under which it characterizes steady state behavior. In the special case where the problem is static, equilibrium coincides with the single-agent version of Berk-Nash equilibrium (Esponda and Pouzo (2016)). We also discuss subtle issues that arise exclusively in dynamic settings due to the possibility of a negative value of experimentation.
We develop an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff-relevant consequences as a function of actions. We introduce the notion of a Berk-Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback-Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players have correctly-specified models. We provide a learning foundation for Berk-Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.