arXiv subjects

Philipp Strack

Publications and source records attributed to Philipp Strack.

At least 19 recordsLinked to original sources

arXiv2026

Sharp Tail Bounds Beyond Twice the Mean

Consider $n$ independent, non-negative, mean at most one random variables, $X_1,X_2,\ldots$. We show the following bound on the probability of their sum exceeding a threshold $t$: \[ \mathbb{P}\left[\sum_{i=1}^n X_i\ge t\right] \leq 1-\left(1-\frac{1}{t}\right)^n \text{ for all } t\ge 2n+1 \,. \] To prove this, we consider a relaxed optimization problem over a set of sequences of ordered, but non-independent random variables. This allows us to reformulate it recursively as dynamic programming problem. The bound becomes an equality for the binary i.i.d.~random variables satisfying $\mathbb{P}\left[X_i=0\right]= 1-\frac{1}{t}$ and $\mathbb{P}\left[X_i=t\right]=\frac{1}{t}$, which remains the maximizer in the relaxed problem.

math.PR↗

arXiv2026

Learning Through Imitation: An Experiment

We compare how well agents aggregate information in two repeated social learning environments. In the first setting agents have access to a public data set. In the second they have access to the same data, and also to the past actions of others. Despite the fact that actions contain no additional payoff-relevant information, and despite potential herd behavior, free riding and information overload issues, observing and imitating the actions of others leads agents to take the optimal action more often in the second setting. We also investigate the effect of group size, as well as a setting in which agents observe private data and others' actions.

econ.TH↗

arXiv2025

Non-Discriminatory Personalized Pricing

A monopolist offers personalized prices to consumers with unit demand, heterogeneous values, and idiosyncratic costs, who differ in a protected characteristic, such as race or gender. The seller is subject to a non-discrimination constraint: consumers with the same cost, but different characteristics must face identical prices. Such constraints arise in regulated markets like credit or insurance. The setting reduces to an optimal transport, and we characterize the optimal pricing rule. Under this rule, consumers may retain surplus, and either group may benefit. Strengthening the constraint to cover transaction prices redistributes surplus, harming the low-value group and benefiting the high-value group.

econ.TH↗

arXiv2024

Entropy-Regularized Optimal Transport in Information Design

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.

math.NA↗

arXiv2024

The Extreme Points of Fusions

Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the connection between Lipschitz-exposed points (measures that are unique optimizers of Lipschitz-continuous objectives) and power diagrams, which are divisions of a space into convex polyhedral ``cells'' according to a weighted proximity criterion. These objects are frequently seen in nature--in cell structures in biological systems, crystal and plant growth patterns, and territorial division in animal habitats--and, as we show, provide the essential structure of Lipschitz-exposed fusions. We apply our results to several questions concerning categorization.

econ.TH↗

arXiv2021

Learning in Repeated Interactions on Networks

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.

econ.TH↗

arXiv2021

Monotone additive statistics

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 nonexpected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.

econ.TH↗

arXiv2021

Optimal Disclosure of Information to a Privately Informed Receiver

We study information design settings where the designer controls information about a state, and there are multiple agents interacting in a game who are privately informed about their types. Each agent's utility depends on all agents' types and actions, as well as (linearly) on the state. To optimally screen the agents, the designer first asks agents to report their types and then sends a private action recommendation to each agent whose distribution depends on all reported types and the state. We show that there always exists an optimal mechanism which is laminar partitional. Such a mechanism partitions the state space for each type profile and recommends the same action profile for states that belong to the same partition element. Furthermore, the convex hulls of any two partition elements are such that either one contains the other or they have an empty intersection. In the single-agent case, each state is either perfectly revealed or lies in an interval in which the number of different signal realizations is at most the number of different types of the agent plus two. A similar result is established for the multi-agent case. We also highlight the value of screening: without screening the best achievable payoff could be as low as one over the number of types fraction of the optimal payoff. Along the way, we shed light on the solutions of optimization problems over distributions subject to a mean-preserving contraction constraint and additional side constraints, which might be of independent interest.

econ.TH↗

arXiv2020

Background risk and small-stakes risk aversion

We show that under plausible levels of background risk, no theory of choice under risk -- such as expected utility theory, prospect theory, or rank dependent utility -- can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) they respect stochastic dominance, and (iii) they account for background risk.

econ.TH↗

arXiv2019

Overconfidence and Prejudice

We explore conclusions a person draws from observing society when he allows for the possibility that individuals' outcomes are affected by group-level discrimination. Injecting a single non-classical assumption, that the agent is overconfident about himself, we explain key observed patterns in social beliefs, and make a number of additional predictions. First, the agent believes in discrimination against any group he is in more than an outsider does, capturing widely observed self-centered views of discrimination. Second, the more group memberships the agent shares with an individual, the more positively he evaluates the individual. This explains one of the most basic facts about social judgments, in-group bias, as well as "legitimizing myths" that justify an arbitrary social hierarchy through the perceived superiority of the privileged group. Third, biases are sensitive to how the agent divides society into groups when evaluating outcomes. This provides a reason why some ethnically charged questions should not be asked, as well as a potential channel for why nation-building policies might be effective. Fourth, giving the agent more accurate information about himself increases all his biases. Fifth, the agent is prone to substitute biases, implying that the introduction of a new outsider group to focus on creates biases against the new group but lowers biases vis a vis other groups. Sixth, there is a tendency for the agent to agree more with those in the same groups. As a microfoundation for our model, we provide an explanation for why an overconfident agent might allow for potential discrimination in evaluating outcomes, even when he initially did not conceive of this possibility.

econ.TH↗

arXiv2019

Testing the Drift-Diffusion Model

The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that corresponds to that boundary. This model has been widely used in psychology, neuroeconomics, and neuroscience to explain the observed patterns of choice and response times in a range of binary choice decision problems. This paper provides a statistical test for DDM's with general boundaries. We first prove a characterization theorem: we find a condition on choice probabilities that is satisfied if and only if the choice probabilities are generated by some DDM. Moreover, we show that the drift and the boundary are uniquely identified. We then use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic.

econ.EM↗

arXiv2019

From Blackwell Dominance in Large Samples to Renyi Divergences and Back Again

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Renyi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Renyi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Renyi divergences.

math.ST↗

arXiv2019

Identifying Present-Bias from the Timing of Choices

Timing decisions are common: when to file your taxes, finish a referee report, or complete a task at work. We ask whether time preferences can be inferred when \textsl{only} task completion is observed. To answer this question, we analyze the following model: each period a decision maker faces the choice whether to complete the task today or to postpone it to later. Cost and benefits of task completion cannot be directly observed by the analyst, but the analyst knows that net benefits are drawn independently between periods from a time-invariant distribution and that the agent has time-separable utility. Furthermore, we suppose the analyst can observe the agent's exact stopping probability. We establish that for any agent with quasi-hyperbolic $\beta,\delta$-preferences and given level of partial naivete $\hat{\beta}$, the probability of completing the task conditional on not having done it earlier increases towards the deadline. And conversely, for any given preference parameters $\beta,\delta$ and (weakly increasing) profile of task completion probability, there exists a stationary payoff distribution that rationalizes her behavior as long as the agent is either sophisticated or fully naive. An immediate corollary being that, without parametric assumptions, it is impossible to rule out time-consistency even when imposing an a priori assumption on the permissible long-run discount factor. We also provide an exact partial identification result when the analyst can, in addition to the stopping probability, observe the agent's continuation value.

econ.TH↗

arXiv2018

The Cost of Information: The Case of Constant Marginal Costs

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.

econ.TH↗

arXiv2018

Matching in Dynamic Imbalanced Markets

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 generate by facilitating future matchings. We prove that this trade-off between a ``thicker'' market and faster matching vanishes in large markets; A 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 (1.6\% more than monthly-batching), and shorter patient waiting times.

econ.TH↗

arXiv2018

Stochastic Dominance Under Independent Noise

Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor risk, house price risk, etc.) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second order stochastic dominance, and show how they lead to a novel, and elementary, axiomatization of mean-variance preferences.

math.PR↗

arXiv2016

Quantum-optical magnets with competing short- and long-range interactions: Rydberg-dressed spin lattice in an optical cavity

The fields of quantum simulation with cold atoms [1] and quantum optics [2] are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities [3,4] lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range -mediated by a quantized optical light field- were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms $N\rightarrow\infty$, (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice [5] coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice Master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field can coexist with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.

cond-mat.quant-gas↗

arXiv2016

Many-Body Quantum Optics with Decaying Atomic Spin States: ($\gamma$, $\kappa$) Dicke model

We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to spontaneous emission with rate $\gamma$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $\kappa$, which is composed of individual atomic decay processes and a collective atomic decay mechanism. The strength of the latter is determined by the cavity geometry. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\rightarrow \infty$. Although $\gamma$ does not conserve the total angular momentum of the spin array, we argue that our solution is exact in the thermodynamic limit, for the number of atoms $N\rightarrow \infty$. In light of recent and upcoming experiments realizing superradiant phase transitions using internal atomic states with pinned atoms in optical lattices, our work lays the foundation for the pursuit of a new class of open quantum magnets coupled to quantum light.

cond-mat.quant-gas↗