Abstracts:  In the second part of our journey through catastrophic collapses in complex systems we will address the potential existence and detection of early-warning signals (EWS). Albeit lacking a rigorous definition, EWS are usually interpreted as “simple properties that change in characteristic ways prior to a critical transition”. A mathematical framework to derive and identify EWS has only been formalised in 2011 and since then some progress has been made. We will thus review the latest developments in the literature as well as establishing mathematical justification for EWS to exist and be detected from raw timeseries data. In conclusion we will briefly understand how some tools from statistical physics can be used to infer the probability of tipping events in simplified stochastic models.

Abstract: In this paper, we present a simple theoretical model of firm pricing with consumer search. A finite number of firms, who offer a homogeneous good, set prices. A continuum of consumers with heterogeneous search costs have information about the distribution of prices; on the basis of this, they search sequentially. Our first result is a simplicity result: in our baseline model, firms face demand functions analogous to those in a differentiated Bertrand model, where demand is related to the number of firms and the search cost parameter. The simplicity of our result allows the model to be used as a ‘workhorse model’, which potentially can be applied to address a range of questions arising in markets characterised by consumer search. We present one such application, using our baseline model to analyse incentives by firms to obfuscate. We also consider a range of extensions to the baseline model.

Abstract: We reappraise the Arrow problem by studying the aggregation of choice functions. We do so in the general framework of judgment aggregation, in which choice functions are naturally representable by specifying, for each menu A and each alternative x in A, whether x is choosable from A, or not. Our framework suggests a natural strengthening of Arrow’s independence condition positing that the collective choosability of an alternative from a menu depends on the individual views on that issue, and that issue alone. Our analysis reveals that Arrovian impossibility results crucially hinge on what internal consistency requirements we impose on choice functions. While aggregation of binary choice functions, satisfying both contraction (α) and expansion (γ) consistency, is necessarily dictatorial, possibilities in the form of oligarchic rules emerge for path-independent choice functions (that is, when the expansion property γ is replaced by the Aizerman condition). When giving up (expansion) consistency conditions altogether, quota rules are possible.