We consider models of growing multilevel systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new agent being attached to a contestant agent at the best hierarchy level (a level nearest to the tree root). The proposed evolution reflects limited information on system properties available to new agents. It can also be expressed in terms of population dynamics. Two models are studied in details: a constant tournament (CT) model wherein the number of tournament participants is constant throughout system evolution, and a proportional tournament (PT) model where this number increases proportionally to the growing size of the system itself. The results of analytical calculations based on a rate equation fit well to numerical simulations for both models. In the CT model all hierarchy levels emerge, but the birth time of a consecutive hierarchy level increases exponentially or faster for each new level. The number of agents at the first hierarchy level grows logarithmically in time, while the size of the last, “worst” hierarchy level oscillates quasi-log-periodically. In the PT model, the occupations of the first two hierarchy levels increase linearly, but worse hierarchy levels either do not emerge at all or appear only by chance in the early stage of system evolution to further stop growing at all.
The results allow us to conclude that information available to each new agent in tournament dynamics restrains the emergence of new hierarchy levels and that it is the absolute amount of information, not relative, which governs such behaviour: the larger the amount of available information, the slower the growth of consecutive hierarchies. This behaviour resembles models of group cooperation, where easy access to information causes a hierarchy to become shallower provided that system resources are evenly distributed.
Reference: A. Czaplicka, K. Suchecki, B. Minano, M. Trias, and J. A. Hołyst,
PHYSICAL REVIEW E 89, 062810 (2014) http://www.if.pw.edu.pl/~jholyst/data/Information%20slows%20down%20hierarchy%20growth.pdf
Professor Dr. Janusz A. Holyst (*1955) is a Full Professor at Faculty of Physics, Warsaw University of Technology where he leads a Center of Excellence of Complex Systems Reearch. His current research fields include data mining for social groups, models of emotions in cybercommunities, economic and social networks, collective bankruptcies, collective opinion formation, nonequilibrium statistical physics, cellular automata, self- organized criticality and phase transitions. He is one of the pioneers in applying physical methods to economical and social systems and is the Co-Founder and Chairman of the Section Physics in Economy and Social Sciences of Polish Physical Society. He coordinated several international projects, including Cyberemotions (www.cyberemotions.eu) and RENOIR (www.renoirproject.eu), and was a scientific advisor of 12 completed Ph.D. thesis on nonlinear dynamics and complex systems. He collaborates with several research institutes including Stanford, NTU, and ETH. His list of publications includes over 150 papers (www.if.pw.edu.pl/ jholyst) in peer reviewed journals that have been cited over 2600 times.
Faculty of Physics, Center of Excellence for Complex Systems Research,
Warsaw University of Technology