# papers in progress

**Memory**

Economic modelers have struggled with incorporating the limits of human memory into their models in ways that are tractable, realistic, and make good testable predictions about human behavior. In this paper, we bring together tools and results from neuroscience, coding theory, and the rational inattention literature in order to create a model of costly memory. In this model, players select costly memory plans which they use to retain information that they expect will be useful in the future. The plans are selected rationally in order to maximize expected payoffs from informed choices net the cost of the memory plan. We discuss both a general memory cost model and a more specific one based on storing information as strings of decaying bits. In the context of the general model, we consider how principals can profitably persuade agents using only the timing of information release. In the context of the coding based model, we show that rational memory with decay can predict a number of interesting economic phenomena. For example, events that occur close to elections have disproportionately large impacts on voting behavior. In insurance markets Kunreuther et al. (2013) describe the phenomenon of “insurance cycles”, whereby individuals buy insurance after a disaster, then let it lapse when no further disasters are forthcoming. We conclude the paper with a discussion of how the model can be enriched to be consistent with the psychological and neuro-scientific memory literature.

**Rational Inattention**

**Experimental Tests of Rational Inattention**** **(with Mark Dean)

We use laboratory experiments to test models of ‘rational inattention,’ in which people acquire information to maximize utility from subsequent choices net of information costs. We show that subjects adjust their attention in response to changes in incentives a manner which is broadly in line with the rational inattention model but which violates models such as random utility in which attention is fixed. However, our results are not consistent with information costs based on Shannon entropy, as is often assumed in applied work. We find more support for a class of ‘posterior separable’ cost functions which generalize the Shannon model.

**Estimating Information Cost Functions in Models of Rational Inattention** (with Ambuj Dewan)

In models of rational inattention, information costs are usually modeled using mutual information, which measures the expected reduction in entropy between prior and posterior beliefs, or ad hoc functional forms, but little is known about what form these costs take in reality. We show that under mild assumptions on information cost functions, including continuity and convexity, gross payoffs to decision makers are non-decreasing and continuous in potential rewards. We conduct laboratory experiments consisting of simple perceptual tasks with fine-grained variation in the level of potential rewards that allow us to test several hypotheses about rational inattention and compare various models of information costs via information criteria. We find that most subjects exhibit monotonicity in performance with respect to potential rewards, and there is mixed evidence on continuity and convexity of costs. Moreover, a significant portion of subjects are likelier to make small mistakes than large ones, contrary to the predictions of mutual information. This suggests that while people are generally rationally inattentive, their cost functions may display non-convexities or discontinuities, or they may incorporate some notion of perceptual distance. The characteristics of a decision-maker’s information cost function have implications for various economic applications, including investment.

Rational Attention with Perceptual Distances (with Ambuj Dewan)

In recent years, a great deal of work has been done on the idea of rational attention, the concept that people can rationally choose the type of quality of signal they receive about the world with more informative signals being more costly. Thus far, however, most models of rational inattention have not been able to incorporate perceptual distance, ie the fact that some states of nature are easier to distinguish than others. In this paper, we will be proposing and testing a number of models of rational attention which incorporate perceptual distance. We consider models based on normal signals, Markov transition matrices, and several models in which the probability of confusing two states is a fixed function of their distance under some metric. The models are tested and compared using data from incentivized dot counting and angle differentiation tasks.

**Network Formation**

Centrality in a network is highly valuable. This paper investigates the idea that the timing of entry into the network is a crucial determinant of a node's final centrality. We propose a model of strategic network growth which makes novel predictions about the forward-looking behaviors of players. In particular, the model predicts that agents entering the network at specific times will "vie for dominance"; that is they will make more connections than is myopically optimal in hopes of receiving additional connections from future players and thereby becoming dominant. The occurrence of these opportunities varies non monotonically with the parameters of the game. In a laboratory experiment, we find that players do exhibit “vying for dominance” behavior, but do not always do so at the predicted critical times. We find that a model of heterogeneous risk aversion best fits the observed deviations from initial predictions. Timing determines whether players have the opportunity to become dominant, but individual characteristics determine whether players exploit that opportunity.

The Theory of Vying for Dominance in Dynamic Network Formation

In many networks, a few highly central nodes have outsized impacts on the structure of the network and generate a large amount of value, but what determines which nodes become central? We hypothesize that the timing of entry into the network can also play a critical role. In this paper, we present a new dynamic model of network formation with history dependence, growth, and forward looking strategic agents. These features increase the importance of importance of the dynamics and generate novel strategic behaviors such as “vying for dominance,” making a larger number of connections than is myopically beneficial in expectation of receiving more connections from future players. Due to the strategic richness, the model rapidly becomes intractable as the size of the network increases. However, if we restrict the model such that players must connect to one of the most central nodes as they join the network, we can restore tractability, and we find that all players either vying for dominance or playing myopically. Furthermore, if we assume players use a novelty seeking tie-breaking rule, players vie for dominance periodically, the solution is characterized by periodic vying for dominance separated by periods of low connection myopic play. Because vying becomes more expensive as the network grows, the time between vying agents increases exponentially over time.