We use simulations of a simple learning model to predict cooperation rates in the experimental play of the indefinitely repeated prisoner’s dilemma. We suppose that learning and the game parameters only influence play in the initial round of each supergame, and that after these rounds, play depends only on the outcome of the previous round. We find that our model predicts out-of-sample cooperation at least as well as models with more parameters and harder-to-interpret machine learning algorithms. Our results let us predict the effect of session length and help explain past findings on the role of strategic uncertainty. (JEL C57, C72, C73, D83, D91)

We predict cooperation rates across treatments in the experimental play of the indefnitely repeated prisoner’s dilemma using simulations of a simple learning model. We suppose that learning and the game parameters only infuence play in the initial round of each supergame. Using data from 17 papers, we fnd that our model predicts out-of-sample cooperation at least as well as more complicated models with more parameters and machine learning algorithms. Our results let us predict how cooperation rates change with longer experimental sessions, and explain and sharpen past fndings on the role of strategic uncertainty.

We predict cooperation rates across treatments in the experimental play of the indefinitely repeated prisoner’s dilemma using simulations of a simple learning model. We suppose that learning and the game parameters only influence play in the initial round of each supergame. Using data from 17 papers, we find that our model predicts out-of-sample cooperation at least as well as more complicated models with more parameters and harder-to-interpret machine learning algorithms. Our results let us predict how cooperation rates change with longer experimental sessions, and help explain past findings on the role of strategic uncertainty.

Insights from behavioral economics suggest that perfect rationality is an insufficient model of human decision-making. However, the empirically observed deviations from perfect rationality or biases vary substantially among environments. There is, therefore, a need for theories that inform us when and how we should expect deviations from rational behavior. We suggest that such a theory can be found by assuming optimal use of limited cognitive resources. In this paper, we present a theory of human behavior in one-shot interactions based on the rational use of heuristics. We test our theory by defining a broad family of heuristics for one-shot games and associated cognitive cost functions. In a large, preregistered experiment, we find that behavior is well predicted by our theory, which yields better predictions than existing models. We find that the participants’ actions depend on their environment and previous experiences, in the way the rational use of heuristics suggest.

We introduce and study a model of long-run convention formation for rare interactions. Players in this model form beliefs by observing a recency-weighted sample of past interactions, to which they noisily best respond. We propose a continuous state Markov model, well-suited for our setting, and develop a methodology that is relevant for a larger class of similar learning models. We show that the model admits a unique asymptotic distribution which concentrates its mass on some minimal CURB block configuration. In contrast to existing literature of long-run convention formation, we focus on behavior inside minimal CURB blocks and provide conditions for convergence to (approximate) mixed equilibria conventions inside minimal CURB blocks.

We propose a simple learning model to predict cooperation rates across treatments in the experimental play of the indefinitely repeated prisoner’s dilemma. Using data from 28 treatments gathered from 16 papers, we find that our 6 parameter model performs at least as well as more complicated models and better than machine learning algorithms. We find that learning has the most effect on choices in the initial round of each supergame, and that whether cooperation rises or falls in the course of a session depends on the way the initial choices in a supergame determine play in subsequent rounds. Our results also explain and sharpen past findings on the role of strategic uncertainty.

Spectral properties of the Schrödinger operator on a finite compact metric graph with delta-type vertex conditions are discussed. Explicit estimates for the lowest eigenvalue (ground state) are obtained using two different methods: Eulerian cycle and symmetrization techniques.