Philipp Strack Publications

We study how long-lived, rational agents learn in a social network. In every period, after observing the past actions of his neighbors, each agent receives a private signal, and chooses an action whose payoff depends only on the state. Since equilibrium actions depend on higher-order beliefs, it is difficult to characterize behavior. Nevertheless, we show that regardless of the size and shape of the network, the utility function, and the patience of the agents, the speed of learning in any equilibrium is bounded from above by a constant that only depends on the private signal distribution.

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated-utility” models, and extend our analysis to outcomes that are perceived to follow a Markov process.

We study a generalization of the classical monopoly insurance problem under adverse selection (see Stiglitz 1977) where we allow for a random distribution of losses, possibly correlated with the agent's risk parameter that is private information. Our model explains patterns of observed customer behavior and predicts insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs or menus of insurance with coverage limits–premium pairs. A main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility functional (Yaari 1987).

A signal is privacy-preserving with respect to a collection of privacy sets, if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy-preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy-preserving if and only if it is a garbling of a reordered quantile signal. These signals are equivalent to couplings, which in turn lead to a characterization of optimal privacy-preserving signals for a decision-maker. We demonstrate the applications of this characterization in the contexts of algorithmic fairness, price discrimination, and information design.

We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with Blackwell monotonicity and a continuity condition, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states.

We study dynamic matching in exchange markets with easy- and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents provide by facilitating future matchings. We prove that the trade-off between a “thicker” market and faster matching vanishes in large markets; the greedy policy leads to shorter waiting times and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly used policies (1.8% more than monthly batching) and shorter waiting times (16 days faster than monthly batching).

We model an agent who stubbornly underestimates how much his behavior is driven by undesirable motives, and, attributing his behavior to other considerations, updates his views about those considerations. We study general properties of the model, and then apply the framework to identify novel implications of partially naive present bias. In many stable situations, the agent appears realistic in that he eventually predicts his behavior well. His unrealistic self-view does, however, manifest itself in several other ways. First, in basic settings he always comes to act in a more present-biased manner than a sophisticated agent. Second, he systematically mispredicts how he will react when circumstances change, such as when incentives for forward-looking behavior increase or he is placed in a new, ex-ante identical environment. Third, even for physically non-addictive products, he follows empirically realistic addiction-like consumption dynamics that he does not anticipate. Fourth, he holds beliefs that — when compared to those of other agents — display puzzling correlations between logically unrelated issues. Our model implies that existing empirical tests of sophistication in intertemporal choice can reach incorrect conclusions. Indeed, we argue that some previous findings are more consistent with our model than with a model of correctly specified learning.

We consider the optimal taxation of a good which exhibits a negative externality, in a setting where agents differ in their value for the good, their disutility from the externality, and their value for money, while the planner observes neither. Pigouvian taxation is the unique Pareto efficient mechanism, yet it is only optimal if the planner puts higher Pareto weights on richer agents. We derive the optimal tax schedule for both a narrow allocative objective and a utilitarian objective for the planner. The optimal tax is generically nonlinear, and Pareto inefficient. The optimal mechanism might take a “non-market” form and cap consumption, or forbid it altogether. We illustrate the tractability of our model by deriving closed form solutions for the lognormal and Rayleigh distribution. Finally, we calibrate our model and derive optimal taxes for the case of air travel.

We study dynamic matching in exchange markets with easy- and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents provide by facilitating future matchings. We prove that the trade-off between a “thicker” market and faster matching vanishes in large markets; the greedy policy leads to shorter waiting times and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly used policies (1.8% more than monthly batching) and shorter waiting times (16 days faster than monthly batching).