Abstract

We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge production, firms follow different strategies to create and/or to delete links with other firms. Dependent on the information firms take into account for their decision, we find the emergence of different network structures. We analyze the conditions for the existence of these structures within a mathematical approach and underpin our findings by extensive computer simulations which show the evolution of the networks and their equilibrium state. In the discussion of the results, particular attention is given to the emergence of direct and indirect reciprocity in knowledge exchange, which refers to the emergence of cycles in the network structure. In order to motivate our modeling framework, in the first part of the chapter we give a broad overview of existing literature from economics and physics. This shows that our framework bridges and extends two different lines of research, namely the study of equilibrium networks with simple topologies and the dynamic approach of hypercycle models.

Abstract

Networks play an important role in a wide range of economic phenomena. Despite this fact, standard economic theory rarely considers economic networks explicitly in its analysis. However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. This recent development has lead to a fast increase in theoretical research on economic networks. In this tutorial, we introduce the reader to some basic concepts used in a wide range of models of economic networks.

Abstract

We investigate some of the properties and extensions of a dynamic innovation network model recently introduced in [Koenig et al. Games and Eco. Beh. 75-2 p694-p713 (2012)]. In the model, the set of efficient graphs ranges, depending on the cost for maintaining a link, from the complete graph to the (quasi-) star, varying within a well defined class of graphs. However, the interplay between dynamics on the nodes and topology of the network leads to equilibrium networks which are typically not efficient and are characterized, as observed in empirical studies of R&D networks, by sparseness, presence of clusters and heterogeneity of degree. In this paper, we analyze the relation between the growth rate of the knowledge stock of the agents from R&D collaborations and the properties of the adjacency matrix associated with the network of collaborations. By means of computer simulations we further investigate how the equilibrium network is affected by increasing the evaluation time $ tau$ over which agents evaluate whether to maintain a link or not. We show that only if $ tau$ is long enough, efficient networks can be obtained by the selfish link formation process of agents, otherwise the equilibrium network is inefficient. This work should assist in building a theoretical framework of R&D networks from which policies can be derived that aim at fostering efficient innovation networks.

Abstract

In this chapter, we present a model recently introduced in [14, 16] and we discuss the features of a networked economy in which N firms are organised in M production levels. Each firm at a certain level is supplied by a subset of firms in the upper level (suppliers) and supplies a subset of the firms in the lower level (customers). The bottom level consists of retailers, i.e., firms that sell in the consumer market. The top level consists of firms that provide primary goods to the other firms. Firms are connected by means of two mech-anisms: (i) the output of supplier firms is an input for customer firms; (ii) supplier firms extend trade credit to customers (as it is typically the case in reality). However, in the model, the trade credit contract is only implicitly sketched: we neither design the optimal trade credit scheme nor look for the optimal amount of trade credit a customer firm should require. Instead, we focus on the mechanisms of propagation of bankruptcy .

Abstract

We propose a methodological framework to study the dynamics of inter-regional investment flow in Europe from a Complex Networks perspective, an approach with recent proven success in many fields including economics. In this work we study the network of investment stocks in Europe at two different levels: first, we compute the inward-outward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inward-outward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. Despite the intuitive value of this approach for EU policy making in economic development, to our knowledge there are no similar works in the literature yet. In this paper we focus on statistical distributions and scaling laws of activity, investment stock and connectivity degree both at the level of firms and at the level of regions. In particular we find that investment stock of firms is power law distributed with an exponent very close to the one found for firm activity. On the other hand investment stock and activity of regions turn out to be log-normal distributed. At both levels we find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales with connectivity in a similar way as has been previously found for stock market data, calling for further investigations on a possible general scaling law holding true in economical networks.

Abstract

We investigate the dynamics of the creation, development, and breakup of social networks formed by coalitions of agents. As an application, we consider coalition formation in a consumer electronic market. In our model, agents have benefits and costs from establishing a social network by participating in a coalition. Buyers benefit in terms of volume discount and better match of their preferences. Sellers benefit in terms of better predictability of sales volumes. The model allows us to investigate the stability and size of the coalitions as well as the performance of the market in terms of utility of the agents. We find that the system exhibits three different dominating regimes: individual purchasing behaviour, i.e., no social network exists among the agents, formation of several heterogenous coalitions, i.e., a number of social networks which are not connected, as well as condensation to a giant coalition, i.e., a social network involving all agents.

Abstract

We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represented by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows an eigendynamics based on catalytic support from other nodes, whereas on a much slower time scale the network evolves through selection and mutation of its nodes-agent. In the first part of the paper, we explain the dynamics of the model by means of characteristic snapshots of the network evolution and confirm earlier findings on crashes and recoveries in the network structure. In the second part, we focus on the aggregate behavior of the network dynamics. We show that the disruptions in the network structure are smoothed out, so that the average evolution can be described by a growth regime followed by a satura-tion regime, without an initial random regime. For the saturation regime, we obtain a logarithmic scaling between the average connectivity per node ls and a parameter m, describing the average incoming connectivity, which is independent of the system size N.

Abstract

As networks and their structure have become a major field of research, a strong demand for network visualization has emerged. We address this challenge by formalizing the well established spring layout in terms of dynamic equations. We thus open up the design space for new algorithms. Drawing from the knowledge of systems design, we derive a layout algorithm that remedies several drawbacks of the original spring layout. This new algorithm relies on the balancing of two antagonistic forces. We thus call it $$em arf for "attractive and repulsive forces". It is, as we claim, particularly suited for a dynamic layout of smaller networks ($n < 10^3$). We back this claim with several application examples from on going complex systems research.