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We show that the treatment effect estimated by standard methods such as regression discontinuity analysis or difference-in-differences may contain a transient “learning effect” that is entangled with the long-term effect of the treatment. This learning effect occurs when the variable of interest is the agents’ efforts, when treatment and control correspond to success or failure: success or failure gives agents information about how much their effort matters, and consequently changes the amount of effort they provide after treatment. We examine the impact of the learning effect and when it is likely to be substantial. (JEL C13, C21, D72, D74, D83, I20)

We present a speculative application of model estimates from Fudenberg and Puri (2021) to prize-linked savings in South Africa. The models used include one combining simplicity theory (Puri 2018, 2022), a preference for lotteries with fewer possible outcomes, with cumulative prospect theory. The results and those of prior literature indicate that both simplicity and probability weighting have a role to play in understanding behavior in choice under risk. We discuss the properties of these models and their implications for behavior.

We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to lotteries, initial play in games, and human generation of random sequences. We discover considerable variation in the completeness of existing models, which sheds light on whether to focus on developing better models with the same features or instead to look for new features that will improve predictions. We also illustrate how and why completeness varies with the experiments considered, which highlights the role played in choosing which experiments to run.

Justified communication equilibrium (JCE) is an equilibrium refinement for signaling games with cheap-talk communication. A strategy profile must be a JCE to be a stable outcome of nonequilibrium learning when receivers are initially trusting and senders play many more times than receivers. In the learning model, the counterfactual “speeches” that have been informally used to motivate past refinements are messages that are actually sent. Stable profiles need not be perfect Bayesian equilibria, so JCE sometimes preserves equilibria that existing refinements eliminate. Despite this, it resembles the earlier refinements D1 and NWBR, and it coincides with them in co-monotonic signaling games. (JEL C70, D82, D83, J23, M51)

We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. When the updating of a player’s record can depend on the actions of both players in a match, any strictly individually rational action can be supported in a steady-state equilibrium. When record updates can depend only on a player’s own actions, fewer actions can be supported. Here, we focus on the prisoner’s dilemma and restrict attention to strict equilibria that are coordination-proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by their records and expected continuation payoffs. Such equilibria can support full cooperation if the stage game is either “strictly supermodular and mild” or “strongly supermodular,” and otherwise permit no cooperation at all. The presence of “supercooperator” records, where a player cooperates against any opponent, is crucial for supporting any cooperation when the stage game is “severe.”

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash equilibrium has positive probability of being the long‐run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

We study the effect of how types are assigned to participants in a signaling-game experiment. The sender has two actions, In and Out, and two types. In one treatment, types are i.i.d. in every period, and senders gather experience with both types. In the other, types are assigned once-and-for-all, and feedback is type specific. The theory of learning in games predicts that the non-Nash but self-confirming equilibrium where some fraction of types play Out can persist in the fixed-type treatment but not when types are i.i.d. Our results confirm that more senders do play Out in the fixed-type treatment. (JEL C92, D82, D83)

We show that the probability that Bayesian posteriors assign to the outcome distributions that do not ``best fi t" the empirical distribution (in terms of Kullback-Leibler divergence) converges to zero at a uniform and exponential rate, even when the prior does not have full support. This extends the uniform convergence result of Diaconis and Freedman (1990), which assumes a full support prior, and lets us provide a rate of convergence for Berk (1966)'s result that the posterior concentrates around the Kullback-Leibler minimizers with respect to the true data generating process. We also extend Diaconis and Freedman (1990) to the case where outcomes are perceived to have a Markov structure.

The drift-diffusion model (DDM) is a model of sequential sampling with diffusion signals, where the decision maker accumulates evidence until the process hits either an upper or lower stopping boundary and then stops and chooses the alternative that corresponds to that boundary. In perceptual tasks, the drift of the process is related to which choice is objectively correct, whereas in consumption tasks, the drift is related to the relative appeal of the alternatives. The simplest version of the DDM assumes that the stopping boundaries are constant over time. More recently, a number of papers have used nonconstant boundaries to better fit the data. This paper provides a statistical test for DDMs with general, nonconstant boundaries. As a by-product, we show that the drift and the boundary are uniquely identified. We use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic based on finite samples.

We analyze situations in which players build reputations for honesty rather than for playing particular actions. A patient player facing a sequence of short-run opponents makes an announcement about their intended action after observing an idiosyncratic shock, and before players act. The patient player is either an honest type whose action coincides with their announcement, or an opportunistic type who can freely choose their actions. We show that the patient player can secure a high payoff by building a reputation for being honest when the short-run players face uncertainty about which of the patient player's actions are currently feasible, but may receive a low payoff when there is no such uncertainty., Working draft

We model the joint distribution of choice probabilities and decision times in binary decisions as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. We show that choices are more likely to be correct when the agent chooses to decide quickly, provided the agent’s prior beliefs are correct. This better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model (DDM), where the agent knows the utility difference between the choices. (JEL C41, D11, D12, D83)

Which equilibria will arise in signaling games depends on how the receiver interprets deviations from the path of play. We develop a micro-foundation for these off-path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises through non-equilibrium learning by populations of patient and long-lived senders and receivers. In our model, young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals as experiments to learn about the behavior of the population of receivers. Differences in the payoff functions of the types of senders generate different incentives for these experiments. Using the Gittins index (Gittins (1979)), we characterize which sender types use each signal more often, leading to a constraint on the receiver's off-path beliefs based on “type compatibility” and hence a learning-based equilibrium selection. ©2018 The Econometric Society, NSF grant (SES 1643517)

We use an evolutionary model to determine what sorts of misperceptions are likely to persist. In our model, every period a new generation of agents uses their subjective models and the outcome distribution induced by the previous generation to update their beliefs about some underlying parameters. Different agents may employ different subjective models and subjective models that induce actions that perform better increase their relative prevalence. To test the stability of steady states, we introduce the possibility that a small fraction of agents enlarges their subjective model in a way that lets them better fit their observations. We characterize which equilibria are resistant to "local mutations'' to a nearby model, and which are resistant to mutations where agents drop one of the hypotheses they had been imposing on their beliefs, e.g. relaxing independence to positive correlation.