General equilibrium is the dominant theoretical framework for economic policy analysis at the level of the whole economy. In practice, general equilibrium treats economies as being always in equilibrium, albeit in a sequence of equilibria as driven by external changes in parameters. This view is sometimes defended on the grounds that internal dynamics are fast, while external changes are slow, so that the economy can be viewed as adjusting instantaneously to any changed conditions. However, the argument has not been presented in a rigorous way. In this paper we show that when conditions are such that: a) economies do respond essentially instantaneously to external influences; b) the external changes are small compared to the values that characterize the economy; and c) the economy's dynamics are continuous and first-order in time (as for Walrasian tatonnement), the resulting economic theory is equivalent to a topological field theory. Because it is a topological theory it has no dynamics in a strict sense, and so perturbatively---that is, when examining dynamics in the region of a critical point---the field theory behaves as general equilibrium posits. However, the field-theoretic form of the theory admits non-perturbative instanton solutions that link different critical points. Thus, in this theory, and in contrast to general equilibrium, the internal dynamics of the model occasionally make an appearance in the form of abrupt, noise-driven transitions between critical points. [more]

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the Random Field Ising model (RFIM) indeed provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilising self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of RFIM-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith's invisible hand can badly fail at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria to be reached. As a theoretical challenge, the study of so-called "detailed-balance" violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic. [more]

For the first time, we apply the wavelet coherence methodology on biofuels (ethanol and biodiesel) and a wide range of related commodities (gasoline, diesel, crude oil, corn, wheat, soybeans, sugarcane and rapeseed oil). This way, we are able to investigate dynamics of correlations in time and across scales (frequencies) with a model-free approach. We show that correlations indeed vary in time and across frequencies. We find two highly correlated pairs which are strongly connected at low frequencies - ethanol with corn and biodiesel with German diesel - during almost the whole analyzed period (2003-2011). Structure of correlations remarkably changes during the food crisis - higher frequencies become important for both mentioned pairs. This implies that during stable periods, ethanol is correlated with corn and biodiesel is correlated with German diesel mainly at low frequencies so that they follow a common long-term trend. However, in the crisis periods, ethanol (biodiesel) is lead by corn (German diesel) even at high frequencies (low scales), which implies that the biofuels prices react more rapidly to the changes in their producing factors. [more]

A central conclusion of the standard theory of consumption is that consumers' preferences can be taken as theoretical primitives. Special categories of consumption, such as "basic needs", or of goods, such as "subsistence goods" are seen as extra theoretical baggage that add few, if any, insights. This theoretical orientation has been absorbed into the theory of aggregate demand, but the aggregate theory has a serious problem that is not shared by the individual-level theory: no matter how well-behaved the individual-level demand functions may be, the aggregate-level function can take on almost any form. This result follows from the SMD theorem, named after Sonnenschein, Mantel, and Debreu, who developed the theory; Kirman and Koch strengthened the results, and the SMD-KK theorem poses a fundamental challenge to models linking micro and macroeconomics. A standard response to the aggregation problem is to introduce a representative agent, but this merely sidesteps the problem. We argue that the aggregation problem arises, in part, because of the exclusion of needs from the theory. Specifically, we argue that material needs--such as basic needs for energy, water, food, and shelter--must be included as theoretical primitives because both the needs and the satisfiers of those needs are universal. We construct a microeconomic model with material needs and show that the form of the aggregate excess demand function is not completely arbitrary, so the SMD-KK theorem does not apply. We discuss the implications of this result. [more]

The structure of a society depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society's hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined hierarchy allows agents to climb it, thus reinforcing it, whereas in a "disordered" society it is harder for agents to find out whom they should connect to in order to become more central. Interestingly, a social order emerges when agents strive harder to climb society and it results in a state of reduced social mobility, as a consequence of ergodicity breaking, where climbing is more difficult. [more]

By analysing the evolution of the street network of Greater London from the late 1700s to the present, we are able to shed light on the inner mechanisms that lie behind the growth of a city. First we define an object called a city as a spatial discontinuous phenomena, from clustering the density of street intersections. Second, we find that the city growth mechanisms can be described by two logistic laws, hence can be determined by a simple model of urban network growth in the presence of competition for limited space. [more]

In standard economic theory, mechanisms like Adam Smith's "invisible hand" or the Walrasian auctioneer balance aggregate demand and supply and match individuals such that the market clears. Usually, some kind of price adjustment process is assumed without specifying how the implied transactions are organized. In real markets, price adjustment and the matching of buyers and sellers involve considerable exchange of information. Past experience plays an important role in partner selection and in deciding whether a suggested transaction is accepted or not. This implies a process of learning about trading partners and opportunities. The model suggested here, explains how this learning leads to market organization (loyality) or a lack thereof (searching). A decentralized market of a perishable good is considered, where past experience governs the choice of trading partner. Depending on how important past payoffs are and how long the memory is, and depending on the number of players in the market, buyers decide to search or to be loyal. The transition from searching to loyality is very abrupt and resembles phase transitions known from statistical physics. Simulations and empirical evidence from the Marseille wholesale fish market confirm the co-existence of the two behavioral patterns of buyers and the importance of past experience of their behavior. [more]

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST-symmetry is spontaneously broken by instantons, which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent modulii of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE's parameters and the criticality is "self-tuned". The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some of SOC's and the concept of topological quantum computing. [more]

Modularity is an important concept in evolutionary theorizing but lack of a consistent definition renders study difficult. Using the generalized NK-model of fitness landscapes, we differentiate modularity from decomposability. Modular and decomposable systems are both composed of subsystems, but in the former, these subsystems are connected via interface standards, while in the latter, subsystems are completely isolated. We derive the optimal level of modularity, which minimizes the time required to globally optimize a system, both for the case of two-layered systems and for the general case of multi-layered hierarchical systems containing modules within modules. This derivation supports the hypothesis of modularity as a mechanism to increase the speed of evolution. Our formal definition clarifies the concept of modularity and provides a framework and an analytical baseline for further research. [more]

In two previous papers the author developed a second-order price adjustment (t\^atonnement) process. This paper extends the approach to include both quantity and price adjustments. We demonstrate three results: a analogue to physical energy, called "activity" arises naturally in the model, and is not conserved in general; price and quantity trajectories must either end at a local minimum of a scalar potential or circulate endlessly; and disturbances into a subspace of substitutable commodities decay over time. From this we argue, although we do not prove, that the model features global stability, combined with local instability, a characteristic of many real markets. Following these observations and a brief survey of empirical results for price-setting and consumption behavior in markets for "real" goods (as opposed to financial markets), we conjecture that Stigler and Becker's well-known theory of consumer preference opens the possibility of substantial degeneracy in commodity space, and therefore that price and quantity trajectories could lie on a relatively low-dimensional subspace within the full commodity space. [more]