Cartel Pricing Dynamics with Cost Variability and Endogenous Buyer Detection

This paper characterizes collusive pricing patterns when buyers may detect the presence of a cartel. Buyers are assumed to become suspicious when observed prices are anomalous. We find that the cartel price path is comprised of two phases. During the transitional phase, price is generally rising and relatively unresponsive to cost shocks. During the stationary phase, price responds to cost but is much less sensitive than under non-collusion or simple monopoly. The length of the transition phase is decreasing in the variance of cost shocks. It is also shown that the cartel price path may overshoot its long-run level so that price converges from above.

"Cartel Pricing Dynamics with Cost Variability and Endogenous Buyer Detection"

This paper characterizes collusive pricing patterns when buyers may detect the presence of a cartel. Buyers are assumed to become suspicious when observed prices are anomalous. We find that the cartel price path is comprised of two phases. During the transitional phase, price is generally rising and relatively unresponsive to cost shocks. During the stationary phase, price responds to cost but is much less sensitive than under non-collusion or simple monopoly; a low price variance may then be a collusive marker. Compared to when firms do not collude, cost shocks take a longer time to pass-through to price.

he Impact of the Corporate Leniency Program on Cartel Formation and the Cartel Price Path

Previous research exploring the effect of corporate leniency programs has modelled the oligopoly stage game as a Prisoners?Dilemma. Using numerical analysis, we consider the Bertrand price game and allow the probability of detection and penalties to be sensitive to firms?prices. Consistent with earlier results, a maximal leniency program necessarily makes collusion more difficult. However, we also find that partial leniency programs - such as in the U.S. - can make collusion easier compared to offering no leniency. We also show that even if cartel formation is not deterred, a leniency program can reduce the prices charged by firms.

Efficient approximate unitary t-designs from partially invertible universal sets and their application to quantum speedup

At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct new families of quantum circuits on $n$-qubits giving rise to $\varepsilon$-approximate unitary $t$-designs efficiently in $O(n^3t^{12})$ depth. These quantum circuits are based on a relaxation of technical requirements in previous constructions. In particular, the construction of circuits which give efficient approximate $t$-designs by Brandao, Harrow, and Horodecki (F.G.S.L Brandao, A.W Harrow, and M. Horodecki, Commun. Math. Phys. (2016).) required choosing gates from ensembles which contained inverses for all elements, and that the entries of the unitaries are algebraic. We reduce these requirements, to sets that contain elements without inverses in the set, and non-algebraic entries, which we dub partially invertible universal sets. We then adapt this circuit construction to the framework of measurement based quantum computation(MBQC) and give new explicit examples of $n$-qubit graph states with fixed assignments of measurements (graph gadgets) giving rise to unitary $t$-designs based on partially invertible universal sets, in a natural way. We further show that these graph gadgets demonstrate a quantum speedup, up to standard complexity theoretic conjectures. We provide numerical and analytical evidence that almost any assignment of fixed measurement angles on an $n$-qubit cluster state give efficient $t$-designs and demonstrate a quantum speedup.Comment: 25 pages,7 figures. Comments are welcome. Some typos corrected in newest version. new References added.Proofs unchanged. Results unchange

Minkowski sums and Hadamard products of algebraic varieties

We study Minkowski sums and Hadamard products of algebraic varieties. Specifically we explore when these are varieties and examine their properties in terms of those of the original varieties.Comment: 25 pages, 7 figure

Surface study of the (100) and (010) faces of the quasicrystalapproximant Al4(Cr, Fe)

Low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM) results are used to study the pseudo-6-fold nature of the (100) surface of the orthorhombic quasicrystal approximant Al4(Cr, Fe). LEED patterns are also presented from the pseudo-10-fold (010) surface of this material. In each case the results are compared with the known bulk structure of this complex metallic alloy

The over-indebtedness of public servants in South Africa

The global financial crisis of 2008 revealed the substantial over-indebtedness of households across many countries. Over-indebtedness of households is the outcome of the policy of financial liberalisation and deregulation since the 1970s. The consumers who are most likely to become over-indebted are employees who earn regular salaries and wages. This paper studies the over-indebtedness of public servants in South Africa. The concept of over-indebtedness is described, as a structural condition of a consumer that experiences financial is unable to repay credit commitments. This paper briefly describes the evolution of consumer credit and discusses the causes and consequences of overindebtedness. The study evaluates the level of over-indebtedness of public servants in South Africa applying three quantitative measures: the ratio of credit repayments to income, the number of credit commitments held by the consumer and the indebtedness index. The analysis uses a very large sample of credit records for public servants that were obtained from a credit bureau shows interesting findings. The overall findings show that majority of public servants in South Africa are over-indebted. The indebtedness index estimates that at least fifty-four (54%) of public servants in South Africa are over-indebted. Although the study did not include any statistical test of significance, the findings of the study are significant given the large sample size. The result should be treated as valid and exploratory