Preferential Urn Model on a Random Network

A preferential urn model on a random network and a complete graph is studied. The preferential urn model is based on the concept "the rich get richer", and has simple dynamics of ball-transfers. The model is considered as a simple socio-economic system. From analytical treatments, it has been revealed that the preferential urn model on the complete graph gives a fat-tailed occupation distribution in the case with randomness for fitness parameters. In the present paper, using numerical experiments, we show that the model on the random network gives a fat-tailed occupation distribution in the case without randomness for fitness parameters; hence, we would consider that the local ball-transfer process on the random network includes effects corresponding to the randomness for fitness parameters. This simple game would give a valuable insight into various phenomena from socio-economic point of view