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Bounded Rationality, Level-k Reasoning, and Cognitive Hierarchies

Paper Session

Friday, Jan. 5, 2018 8:00 AM - 10:00 AM

Pennsylvania Convention Center, 106-B
Hosted By: Econometric Society
  • Chair: Colin F. Camerer, California Institute of Technology

Does the Cognitive Hierarchy Model Describe an Individual's Beliefs? An Experimental Investigation

Daniel Fragiadakis
,
Texas A&M University
David Rojo Arjona
,
University of Leicester

Abstract

Camerer et al. (2004) propose a Cognitive Hierarchy (CH) model that characterizes an individual as a ``step k thinker'' who anticipates a distribution of step 0 through step k players. In a lab experiment, we ask a subject how many participants she believes select each pure strategy in a series of games. We find strong evidence of CH beliefs that are well approximated by normalized Poisson distributions. In addition, we make a methodological contribution to the belief-elicitation literature: our results provide a proof-of-concept that our novel procedure is effective not only in theory, but also in practice.

A Diagnosis on the Relationship Between Equilibrium Play, Stated Beliefs, and Best Responses

Ciril Bosch-Rosa
,
Technical University Berlin

Abstract

Strategic games have two dimensions of difficulty for subjects in the laboratory. One is understanding the rules of the game and forming a best response to whatever beliefs they hold. The other is forming these beliefs correctly. Typically, these two dimensions cannot be disentangled as belief formation crucially depends on the understanding of the game. We present a variation of the Two Player Guessing Game (Grosskopf and Nagel (2008)) which turns an otherwise strategic game into an individual decision-making task. This allows us to perform a within subject analysis of the decisions made for the same ``game'' with and without strategic uncertainty. The results show that subjects with a better score at the individual decision making task form more accurate beliefs of other player's choices, and better-respond to these beliefs. Additionally, we show that those who score higher at our new task modify their beliefs based on the population they play against. This suggests that out of equilibrium play is mostly driven by a limited understanding of the game mechanics.

What Can Be Learned From Behavior? Predictive Ability in Discrete Choice Environments

Maria Jose Boccardi
,
New York University Abu Dhabi

Abstract

Revealed preference restrictions provide testable implications for many theories of consumption behavior. Often, empirical evidence finds violations to the model which raises the question of how severe these are. The severity of the violations does not only depend on the extent of the observed deviations, but also on the sensitivity of the test to detect them if any. This paper provides a joint treatment for the severity of the violations and the sensitivity of the test in discrete choice environments by assessing the amount of information about underlying preference that can be inferred from data while allowing for errors. The proposed approach allows to compare across (limited) data sets and different models of behavior, addressing the concern raised by DeClippel and Rozen (2014) about extensibility of bounded rationality models.

Bounded Rationality And Learning: A Framework and A Robustness Result

J. Aislinn Bohren
,
University of Pennsylvania
Daniel N. Hauser
,
University of Pennsylvania

Abstract

We explore model misspecification in an observational learning framework. Individuals learn from private and public signals and the actions of others. An agent's type specifies her model of the world. Misspecified types have incorrect beliefs about the signal distribution, how other agents draw inference and/or others' payoffs. We establish that the correctly specified model is robust in that agents with approximately correct models almost surely learn the true state asymptotically. We develop a simple criterion to identify the asymptotic learning outcomes that arise when misspecification is more severe. Depending on the nature of the misspecification, learning may be correct, incorrect or beliefs may not converge. Different types may asymptotically disagree, despite observing the same sequence of information. This framework captures behavioral biases such as confirmation bias, false consensus effect, partisan bias and correlation neglect, as well as models of inference, such as level-k and cognitive hierarchy.

Discussant(s)
Stephanie W. Wang
,
University of Pittsburgh
Marina Agranov
,
California Institute of Technology
Annie Liang
,
University of Pennsylvania
Muhamet Yildiz
,
Massachusetts Institute of Technology
JEL Classifications
  • D12 - Consumer Economics: Empirical Analysis
  • C91 - Laboratory, Individual Behavior