arXiv subjects

Andrew Mackenzie

Publications and source records attributed to Andrew Mackenzie.

7 recordsLinked to original sources

arXiv2026

Endogenous shareholding auctions

We introduce endogenous shareholding auctions for production economies where a monopolist must elicit consumer demand in order to determine price and quantity. Each of these auctions has the property that the auction's profit is distributed across the monopolist and the consumers in accordance with ownership shares that are determined over the course of the auction. We characterize this class, and a larger class, on the basis of standard axioms. Finally, we investigate optimal auctions according to both prior-free domination and subjective expected welfare.

econ.TH↗

arXiv2025

Subjective inference

An agent observes a clue, and an analyst observes an inference: a ranking of events on the basis of how corroborated they are by the clue. We prove that if the inference satisfies the axioms of Villegas (1964) except for the classic qualitative probability axiom of monotonicity, then it has a unique normalized signed measure representation (Theorem 1). Moreover, if the inference also declares the largest event equivalent to the smallest event, then it can be represented as a difference between a posterior and a prior such that the former is the conditional probability of the latter with respect to an assessed event that is interpreted as a clue guess. Across these Bayesian representations, the posterior is unique, all guesses are in a suitable sense equivalent, and the prior is determined by the weight it assigns to each possible guess (Theorem 2). However, observation of a prior and posterior compatible with the inference could reveal that all of these guesses are wrong.

econ.TH↗

arXiv2025

Dividing a cake for the irrationally entitled

A perfectly divisible cake is to be divided among a group of agents. Each agent is entitled to a share between zero and one, and these entitlements are compatible in that they sum to one. The mediator does not know the preferences of the agents, but can query the agents to make cuts and appraise slices in order to learn. We prove that if one of the entitlements is irrational, then the mediator must use a protocol that involves an arbitrarily large number of queries in order to construct an allocation that respects the entitlements regardless of preferences.

econ.TH↗

arXiv2023

Patience ensures fairness

We revisit the problem of fairly allocating a sequence of time slots when agents may have different levels of patience (Mackenzie and Komornik 2023). For each number of agents, we provide a lower threshold and an upper threshold on the level of patience such that (i) if each agent is at least as patient as the lower threshold, then there is a proportional allocation, and (ii) if each agent is at least as patient as the upper threshold and moreover has weak preference for earlier time slots, then there is an envy-free allocation. In both cases, the proof is constructive.

econ.TH↗

arXiv2021

Tuning the Fermi Liquid Crossover in Sr$_2$RuO$_4$ with Uniaxial Stress

We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr$_2$RuO$_4$, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasi-particle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi liquid coherence scale is shown to be tunable by strain, and driven to low values as the associated Lifshitz transition is approached.

cond-mat.str-el↗

arXiv2016

Low temperature thermodynamic investigation of the phase diagram of Sr$_3$Ru$_2$O$_7$

We studied the phase diagram of Sr$_3$Ru$_2$O$_7$ by means of heat capacity and magnetocaloric effect measurements at temperatures as low as 0.06 K and fields up to 12 T. We confirm the presence of a new quantum critical point at 7.5 T which is characterized by a strong non-Fermi-liquid behavior of the electronic specific heat coefficient $\Delta$C/T $\sim$ -logT over more than a decade in temperature,placing strong constraints on theories of its criticality. In particular logarithmic corrections are found when the dimension d is equal to the dynamic critical exponent z, in contrast to the conclusion proposed recently [Y. Tokiwa et al., Phys. Rev. Lett. 116, 226402 (2016)]. Moreover, we achieved a clear determination of the new second thermodynamic phase adjoining the first one at lower temperatures. Its thermodynamic features differ significantly from those of the dominant phase and characteristics expected of classical equilibrium phase transitions are not observed, indicating fundamental differences in the phase formation.

cond-mat.str-el↗

arXiv2015

Strain and Vector-Magnetic-Field Tuning of the Anomalous Phase in Sr3Ru2O7

Symmetry is a basic paradigm for analysis of problems in solid state physics, and to controllably break point-group symmetries is a powerful probe of novel forms of order. In this work, we apply two methods, controlled lattice strain and vector magnetic field, to study a well-known correlated electron phase that appears at low temperatures in the layered material Sr3Ru2O7. This phase responds strongly to C4-symmetry-breaking fields, suggesting spontaneous C4 symmetry breaking. However, in this work we find that the data are more easily explained with microscopic coexistence of two orthogonal order parameter components than spontaneous symmetry breaking. The techniques presented in this work will be relevant for other systems where spontaneous C4 symmetry breaking is suspected.

cond-mat.str-el↗