Philipp Strack Publications

We use the tools of mechanism design combined with the theory of risk measures to analyze how a cash-constrained owner of an asset with known, stochastic returns raises capital from a population of investors who differ in their risk aversion and budget constraints. The issuer partitions the asset's cash flow into several asset-backed securities, one for each type of investor. The optimal partition conforms to the commonly observed practice of tranching into senior debt, junior debt, and equity. Tranching arises endogenously due to the differences in risk appetites among agents and in the budget constraints they face.

We study agents who are more likely to remember some experiences than others but update beliefs as if the experiences they remember are the only ones that occurred. To understand the long-run effects of selective memory, we propose selective-memory equilibrium. We show that if the agent’s behavior converges, their limit strategy is a selective-memory equilibrium, and we provide a sufficient condition for behavior to converge. We use this equilibrium concept to explore the consequences of several well-documented biases. We also show that there is a close connection between selective-memory equilibria and the outcomes of misspecified learning.

In this paper, we explore a scenario where a sender provides an information policy and a receiver, upon observing a realization of this policy, decides whether to take a particular action, such as making a purchase. The sender’s objective is to maximize her utility derived from the receiver’s action, and she achieves this by careful selection of the information policy. Building on the work of Kleiner et al., our focus lies specifically on information policies that are associated with power diagram partitions of the underlying domain. To address this problem, we employ entropy-regularized optimal transport, which enables us to develop an efficient algorithm for finding the optimal solution. We present experimental numerical results that highlight the qualitative properties of the optimal configurations, providing valuable insights into their structure. Furthermore, we extend our numerical investigation to derive optimal information policies for monopolists dealing with multiple products, where the sender discloses information about product qualities.

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. Furthermore, distributions of posterior means induced by privacy‐preserving signals are exactly mean‐preserving contractions of that induced by the quantile signal. We discuss the economic implications of our characterization for statistical discrimination, the revelation of sensitive information in auctions and price discrimination.

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non-expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.

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 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 study auction design for bidders equipped with non-expected utility preferences that exhibit constant risk aversion (CRA). The CRA class is large and includes loss-averse, disappointment-averse, mean-dispersion, and Yaari's dual preferences as well as coherent and convex risk measures. Any preference in this class displays first-order risk aversion, contrasting the standard expected utility case which displays second-order risk aversion. The optimal mechanism offers “ full-insurance” in the sense that each agent’s utility is independent of other agents’ reports. The seller excludes less types than under risk neutrality and awards the object randomly to intermediate types. Subjecting intermediate types to a risky allocation while compensating them when losing allows the seller to collect larger payments from higher types. Relatively high types are willing to pay more, and their allocation is efficient.

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).

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem which determines the first time at which the buyer participates in the mechanism. The optimal mechanism thus induces progressive participation by each buyer: he either participates immediately or at a future random time.