What determines the size frequency distribution of β-amyloid (Aβ) deposits in Alzheimer's disease patients?

The factors determining the size of individual β-amyloid (A,8) deposits and their size frequency distribution in tissue from Alzheimer's disease (AD) patients have not been established. In 23/25 cortical tissues from 10 AD patients, the frequency of Aβ deposits declined exponentially with increasing size. In a random sample of 400 Aβ deposits, 88% were closely associated with one or more neuronal cell bodies. The frequency distribution of (Aβ) deposits which were associated with 0,1,2,...,n neuronal cell bodies deviated significantly from a Poisson distribution, suggesting a degree of clustering of the neuronal cell bodies. In addition, the frequency of Aβ deposits declined exponentially as the number of associated neuronal cell bodies increased. Aβ deposit area was positively correlated with the frequency of associated neuronal cell bodies, the degree of correlation being greater for pyramidal cells than smaller neurons. These data suggested: (1) the number of closely adjacent neuronal cell bodies which simultaneously secrete Aβ was an important factor determining the size of an Aβ deposit and (2) the exponential decline in larger Aβ deposits reflects the low probability that larger numbers of adjacent neurons will secrete Aβ simultaneously to form a deposit. © 1995.

Tacit collusion, firm asymmetries and numbers:evidence from EC merger cases

This paper estimates the implicit model, especially the roles of size asymmetries and firm numbers, used by the European Commission to identify mergers with coordinated effects. This subset of cases offers an opportunity to shed empirical light on the conditions where a Competition Authority believes tacit collusion is most likely to arise. We find that, for the Commission, tacit collusion is a rare phenomenon, largely confined to markets of two, more or less symmetric, players. This is consistent with recent experimental literature, but contrasts with the facts on ‘hard-core’ collusion in which firm numbers and asymmetries are often much larger.

Tacit vs. overt collusion firm asymmetries and numbers:what's the evidence?

It is conventional wisdom that collusion is more likely the fewer firms there are in a market and the more symmetric they are. This is often theoretically justified in terms of a repeated non-cooperative game. Although that model fits more easily with tacit than overt collusion, the impression sometimes given is that ‘one model fits all’. Moreover, the empirical literature offers few stylized facts on the most simple of questions—how few are few and how symmetric is symmetric? This paper attempts to fill this gap while also exploring the interface of tacit and overt collusion, albeit in an indirect way. First, it identifies the empirical model of tacit collusion that the European Commission appears to have employed in coordinated effects merger cases—apparently only fairly symmetric duopolies fit the bill. Second, it shows that, intriguingly, the same story emerges from the quite different experimental literature on tacit collusion. This offers a stark contrast with the findings for a sample of prosecuted cartels; on average, these involve six members (often more) and size asymmetries among members are often considerable. The indirect nature of this ‘evidence’ cautions against definitive conclusions; nevertheless, the contrast offers little comfort for those who believe that the same model does, more or less, fit all.

Tacit collusion, firm asymmetries and numbers:evidence from EC merger cases

The purpose of this paper is to identify empirically the implicit structural model, especially the roles of size asymmetries and concentration, used by the European Commission to identify mergers with coordinated effects (i.e. collective dominance). Apart from its obvious policy-relevance, the paper is designed to shed empirical light on the conditions under which tacit collusion is most likely. We construct a database relating to 62 candidate mergers and find that, in the eyes of the Commission, tacit collusion in this context virtually never involves more than two firms and requires close symmetry in the market shares of the two firms.