Critical Nodes In Directed Networks

Critical nodes or "middlemen" have an essential place in both social and economic networks when considering the flow of information and trade. This paper extends the concept of critical nodes to directed networks. We identify strong and weak middlemen. Node contestability is introduced as a form of competition in networks; a duality between uncontested intermediaries and middlemen is established. The brokerage power of middlemen is formally expressed and a general algorithm is constructed to measure the brokerage power of each node from the networks adjacency matrix. Augmentations of the brokerage power measure are discussed to encapsulate relevant centrality measures. We use these concepts to identify and measure middlemen in two empirical socio-economic networks, the elite marriage network of Renaissance Florence and Krackhardt's advice network.Comment: 28 pages, 6 figures, 2 table

Platform Competition as Network Contestability

Recent research in industrial organisation has investigated the essential place that middlemen have in the networks that make up our global economy. In this paper we attempt to understand how such middlemen compete with each other through a game theoretic analysis using novel techniques from decision-making under ambiguity. We model a purposely abstract and reduced model of one middleman who pro- vides a two-sided platform, mediating surplus-creating interactions between two users. The middleman evaluates uncertain outcomes under positional ambiguity, taking into account the possibility of the emergence of an alternative middleman offering intermediary services to the two users. Surprisingly, we find many situations in which the middleman will purposely extract maximal gains from her position. Only if there is relatively low probability of devastating loss of business under competition, the middleman will adopt a more competitive attitude and extract less from her position.Comment: 23 pages, 3 figure

A Belief-based Approach to Network Formation

In this paper we consider four different game-theoretic approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider Jackson-Wolinsky’s concept of pairwise stability. Next, we introduce a stronger version of this concept based on linking decisions by nodes, denoted as strict pairwise stability. Third, we consider Myerson’s consent game and its Nash equilibria. Fourth, within the context of Myerson’s consent game, we consider self-confirming equilibria based on simple myopic belief systems. We provide an exhaustive comparison of the classes of equilibrium networks that result from each of these four approaches. We determine the conditions under which there is equivalence of pairwise stability and strict pairwise stability. Second, we show that the Nash equilibria of Myerson’s consent game form a super set of the class of pairwise stable networks, while strict pairwise stability and monadic stability are fully equivalent.

Stable Networks and Convex Payoffs

Recently a variety of link-based stability concepts have emerged in the literature on game theoretic models of social network formation. We investigate two basic formation properties that establish equivalence between some well known types of stable networks and their natural extensions. These properties can be identified as convexity conditions on the network payoff structures.

Pricing in Economies with a Variable Number of Commodities

We present a general equilibrium model that encompasses the endogenous selection of a set of tradeable commodities. At its foundation we introduce the notion of a trade infrastructure as a set of social institutions describing the trade and production technologies available to the agents in the economy. Our model bridges the analyses of economies with a finite number of commodities and those with an infinite number, and it provides a general framework for investigating a very large class of possible applications. We discuss in detail a simple example on the development of a guild economy into a market based economy. We introduce an equilibrium concept that describes the pricing of trade infrastructures, based on the notion of valuation equilibrium for economies with abstract public goods, as in Diamantaras and Gilles (1996, International Economic Review, 37, 851-860). Through this concept we are able to price the tradeability of a commodity by itself. As our main results we obtain the existence as well as the decentralization of Pareto efficient allocations using the concept of valuation equilibrium. JEL classification: D23, D41, D46, D59, D90, H40, O12Trading systems infrastructures welfare theorems general equilibrium Public economics

The Role of Beliefs and Confidence in Building Social Networks

We examine the process of building social relationships in a non-cooperative game where such link formation is costly and requires mutual consent. We provide a noncooperative foundation for several link-based network stability concepts that have been studied in the literature on network formation. In our model players form myopic beliefs about the feasibility of building direct relationships with their acquaintances. These beliefs represent how each neighbor of a player is expected to respond to the initiation of a link by that player. We introduce a stability concept called “monadic stability” where agents play a best response to their formed myopic beliefs such that these beliefs are self-confirming. The resulting equilibrium networks form a class of networks that are shown to have some very appealing properties.

The Role of Trust in Costly Network Formation

We investigate game theoretic models of entwork formation that are based on individual actions only. Our approach is grounded in three simple and realistic principles. (1) Link formation should be a binary process of consent. (2) Link formation should be costly. (3) The class of network payoff functions should be as general as possible. We provide charecterizations of stable networks under the hypothesis of mutual consent for the case of two-sided and one-sided link formation costs. Furthermore, we introduce a new eqilibrium concept based on a limited, realistic form of farsightedness or (myopic) ''trust'' in network formation. We provide comparisons of the resulting networks with networks satisfying well known stability concepts developed in the literatureSocial networks, individual stability, pairwsie stability, trust

Temporal precedence of emotion over attention modulations in the lateral amygdala: Intracranial ERP evidence from a patient with temporal lobe epilepsy

Previous fMRI studies have reported mixed evidence for the influence of selective attention on amygdala responses to emotional stimuli, with some studies showing "automatic" emotional effects to threat-related stimuli without attention (or even without awareness), but other studies showing a gating of amygdala activity by selective attention with no response to unattended stimuli. We recorded intracranial local field potentials from the intact left lateral amygdala in a human patient prior to surgery for epilepsy and tested, with a millisecond time resolution, for neural responses to fearful faces appearing at either task-relevant or task-irrelevant locations. Our results revealed an early emotional effect in the amygdala arising prior to, and independently of, attentional modulation. However, at a later latency, we found a significant modulation of the differential emotional response when attention was directed toward or away from fearful faces. These results suggest separate influences of emotion and attention on amygdala activation and may help reconcile previous discrepancies concerning the relative responsiveness of the human amygdala to emotional and attentional factors

Field equations and cosmology for a class of nonlocal metric models of MOND

We consider a class of nonlocal, pure-metric modified gravity models which were developed to reproduce the Tully-Fisher relation without dark matter and without changing the amount of weak lensing predicted by general relativity. Previous work gave only the weak field limiting form of the field equations specialized to a static and spherically symmetric geometry. Here we derive the full field equations and specialize them to a homogeneous, isotropic and spatially flat geometry. We also discuss the problem of fitting the free function to reproduce the expansion history. Results are derived for models in which the MOND acceleration a_0 ~ 1.2 x 10^{-10} m/s^{2} is a fundamental constant and for the more phenomenologically interesting case in which the MOND acceleration changes with the cosmological expansion rate.Comment: 15 pages, no figures, uses revtex4, dedicated to Stanley Deser on the occasion of his 83rd birthda