We study a condition of favoring cooperation in a Prisoner's Dilemma game on complex networks. There are two kinds of players: cooperators and defectors. Cooperators pay a benefit b to their neighbors at a cost c, whereas defectors only receive a benefit. The game is a death-birth process with...

The logit function is frequently used in the probabilistic choice problem. The justification is usually provided in a manner that actual utility consists of observed utility and Gumbel random term; the probability then becomes logit. In this paper, we present an alternative explanation of the...

In International Economics, so-called gravity equation has been successful. In the present paper, we show that similar equation concerning transaction network holds well. The weight of transaction network among Japanese prefectures is explained by Sales-i*Sales-j/Distance-ij very well. The...

In this paper, we study imperfect competition on a scale-free network. A scale-free network is not exceptional but rather ubiquitous in reality. For this purpose, we construct a class of utility functions, from which relationships between firms in the form of networks are derived. A regional...

We analyze fundamental characteristics of the inter-firm transaction network through the data of 800,000 Japanese firms. We find that there exists a hierarchical structure and a negative degree correlation in this transaction network. We also find that this undirected network is a scale-free...

We studied how links are formed according to the distance in transaction network of 800,000 firms. We investigated the inter-firm transaction network of $800,000$ firms in Japan. They are almost all firms in Japan. As far as we know, scale-freeness, hierarchy, and degree-degree correlation were...

We analyze fundamental characteristics of the inter-firm transaction network through the data of 800,000 Japanese firms. We find that there exists a hierarchical structure and a negative degree correlation in this transaction network. We also find that this undirected network is a scale-free...

We found hierarchical structure and negative degree correlation in firms' transaction network. The network consists of 800,000 Japanese firms. We also summarize other features of the network and discuss why studying network structure is important. We also found scale free distribution in...