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Rational Inattention with Alternative Cost Functions

Paper Session

Saturday, Jan. 6, 2018 10:15 AM - 12:15 PM

Marriott Philadelphia Downtown, Grand Ballroom Salon C
Hosted By: American Economic Association
  • Chair: Michael Woodford, Columbia University

Coordination and Continuous Choice

Stephen Morris
Princeton University
Ming Yang
Duke University


We study a coordination game where players choose what information to acquire about payoffs prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional defined on information structures. A cost functional satisfies continuous choice if players choose a continuous decision rule even in a decision problem with discontinuous payoffs. If continuous choice holds, there is a unique equilibrium in the coordination game; if continuous choice fails, there are multiple equilibria. We show how continuous choice captures the idea that it is sufficiently harder to distinguish states that are close to each other relative to far away states.

Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy

Andrew Caplin
New York University
Mark Dean
Columbia University
John Leahy
University of Michigan


We introduce analytically tractable new entropy-based attention cost functions. We characterize behaviors consistent with these general models as well as the Shannon model. What makes the Shannon model unique is a "Compression" axiom whereby choices depend only on the probabilistic structure of payoffs, not the nature of the underlying state space.

Rational Inattention with Sequential Information Sampling

Benjamin Hebert
Stanford University
Michael Woodford
Columbia University


We consider optimal information accumulation when a large number of successive
samples of information about a decision situation (each only minimally informative
by itself) can be taken before a decision must be made. At each stage in the sampling
process, many different experiments are possible, and the experimentation undertaken
can also be contingent upon the evidence accumulated to that point. We characterize
information accumulation in a continuous limit of our model, in which both the cost
of individual experiments and the information revealed by each one of them are made
infinitesimal, in terms of a diffusion process on the simplex of posterior distributions
over the possible states. In a broad class of cases, we can establish that the choice
frequencies resulting from optimal information accumulation are the same as those
implied by a static rational inattention problem with a particular static information
cost function. Among the static cost functions that can be grounded in this way is the
mutual information cost function proposed by Sims (2010), but others are possible as
well. We give particular attention to a class of “neighborhood-based” cost functions,
which (unlike mutual information) incorporate a conception of the similarity (or nearness)
of states to one another, and make it more costly to undertake experiments that
can produce different results in similar (but non-identical) states. With this alternative
form of cost function, optimal information accumulation results in choice frequencies
that are similar in similar states; in a continuous-state extension of the model, optimality
implies choice frequencies that vary continuously with the state, even when
the payoffs for given responses jump discontinuously with variation in the state. This
feature of our variant rational inattention model is in conformity with perceptual discrimination

Discrete Choice and Rational Inattention: A General Equivalence Result

Matthew Shum
California Institute of Technology
Andre de Palma
Superior Normal School of Cachan
Mogens Fosgerau
Technical University of Denmark
Emerson Melo
Indiana University-Bloomington


This paper establishes a general equivalence between discrete choice and rational inattention models. Matejka and McKay (2015, AER) showed that when information costs are modeled using the Shannon entropy function, the resulting choice probabilities in the rational inattention model take the multinomial logit form. By exploiting convex-analytic properties of the discrete choice model, we show that when information costs are modeled using a class of generalized entropy functions, the choice probabilities in any rational inattention model are observationally equivalent to some additive random utility discrete choice model and vice versa. This includes empirically relevant specifications such as the probit and nested logit models. Thus any additive random utility model can be given an interpretation in terms of boundedly rational behavior.
Tommaso Denti
Princeton University
Jakub Steiner
Filip Matejka
Philipp Strack
University of California-Berkeley
JEL Classifications
  • D8 - Information, Knowledge, and Uncertainty
  • D1 - Household Behavior and Family Economics