Patent citation networks

Innovation plays a key role in economic development and the patent system is intended (and required by the United States Constitution) to promote {innovation The patent system promotes innovation by giving inventors the power to exclude others from using their inventions during the patent term. The power to exclude is a double-edged sword, however, because it benefits the original inventor, but imposes costs on later innovators seeking to build on past inventions. Thus, the proper design of the patent system is an important matter — and a matter of considerable current debate. The analyis became possible by the existence of the extensive database of citations.

Gábor Csárdi, Katherine J. Strandburg, Jan Tobochnik, and Péter Érdi: The inverse problem of evolving networks: with application to social nets. in: `Handbook of Large-Scale Random Networks’ to be published by Springer Verlag in conjunction with the Bolyai Mathematical Society of Budapest. (Bollobas B, Kozma R eds.)

Dynamic Mechanisms of Public Policy Decision Making Processes: Concepts, Computational Models, and Data Analysis

Bryan D. Jones (University of Washington) Frank R. Baumgartner (Pennsylvania State University) and their co-authors have published a set of research papers focusing on annual budget changes for the past four years. Leptokurtic distribution of percentual budget changes were observed in a broad range of settings: small increases and small decreases of budgets and budget components are the most frequent, but time to time large increases and cut-offs are observed as well. Most frequency distributions appeared as linear on diagrams with double log axes, which strongly suggests a special case of kurtosis, the power-law distribution. They gave detailed explanation both of the possible macroscopic processes and the possible motivations of the more microscopic agents involved in the political decision system in a mathematically non-formalized way.

In our preliminary work we developed their models to get better approximatation of the empirical data. We hope to make progess in this cooperation.

Social networks as evolving complex networks

Social network analysis is focused on searching and finding patterns of people’s interaction and has a grand tradition in sociology. (See International Network for Social Network Analysis (INSNA))

Recently formal models of natural scientists also analyzed the structure of social and related networks (often related to the concepts of “small worlds” and “scale-free” networks) and offered some very abstract developmental models for the evolution of such networks. For more information see:
http://www.santafe.edu/sfi/publications/Bulletins/bulletinFall99/workInProgress/smallWorld.html
http://xxx.lanl.gov/abs/cond-mat/0106096

Our main intention is to narrow the gap between the two perspectives and build realistic models by incorporating elements taken from both bodies of knowledge. While we apply recently elaborated methods in the theory of complex systems, statistical physics and of agent-based simulations of social systems to have a better understanding of the evolution of social networks, we take into account more specific realistic mechanisms for the formation of connections.

The main focus of our research is restricted to the situations, when the nodes (players, agents) are human individuals, but occasionally it might be a firm, country, or other autonomous unit. The restriction appears when we use mostly social psychologically motivated rules for the formation of new and deletion of already existing connections between individuals.

Specifically, we have been developing social netowork models where the nodes represent individuals and the links between nodes represent a friendship connection. Each node is characterized by a trait vector of individuals, and the probability of two nodes forming a connecition depneds on these traits.

Result of this model will be compared to data obtained by studying the friendship-network formed among students at Kalamazoo College. An online survey has been designed incorpoting the expertise of the sociology and psychology department of Kalamazoo College to ask first year students to list their closest friends and to answer questions to categorize personality traits.

Using the data obtained by this survey we wish to reveal the topology of the network and determine how personality traits effect the network structure.

László Zalányi, Gábor Csárdi, Tamás Kiss, Máté Lengyel, Rebecca Warner, Jan Tobochnik and Péter Érdi: Properties of a random attachment growing network Physical Review E 68 066104 (2003)

Minority Game

A minority game is a repeated game where N (odd) players have to choose one out of two alternatives (say A and B) at each time step. Those who happen to be in the minority win. Although being rather simple at first glance this game is subtle in the sense that if all players analyze the situation in the same way, they all will choose the same alternative and will lose. Therefore, players have to be heterogeneous. Moreover, there is a frustration since not all the players can win at the same time: this is an essential mechanism for modelling competition. Note that this is an abstraction of the famous El-Farol’s bar problem (Brian W. Arthur, Am. Econ. Assoc. Papers and Proc 84, 406, (1994)) : in this model, 100 people would like to go to a bar (El Farol) which is too crowded if there are more than 60 people. … (from http://www.unifr.ch/econophysics)

Hierachical extension of the minority game

Csaba Földy, Zoltán Somogyvári, Péter Érdi: Hierarchically Organized Minority Games. Physica A 323 (2003) 735-742