People in some societies tend to put a greater value on equality in distribution of resources even if they have to pay expensive court costs to achieve it, while people in some other societies tend to aim at a maximal share (the whole) but withdraw readily if any conflict occurs. Nash demand game (NDG) is a one-shot two-player game and has been widely used for modeling such bargaining situations in computational and game theoretic approaches. Each player simultaneously demands a portion of some good. If the total amount demanded by the players is less or equal than available good, each player obtains the claimed request. Otherwise, neither player gets anything. Whereas the studies using NDG can account for why people favor the equal distribution, it is too simple to deal with various distributive norms. We use the demand-intensity game (DIG) which adds a psychological factor to NDG while maintaining such simplicity that it can be analyzed by the concepts and tools of the game theory. The goal of this study is to clarify the origin and evolutionary dynamics of distributive norms using DIG. Previous studies have shown that population structures tend to promote cooperative behavior by means of cooperative clustering and assortative interactions. We perform the evolutionary simulation focusing on the effect of the population structures on the evolution of distributive norms. We show a surprising result that network structures significantly change the evolutionary scenario. A population distributed over a regular network tends to evolve a strong equality norm. However, as the random links increase in the network, the more we see the scenario in which monopolists occupy the population who ask for the whole but with a moderate intensity. This result might offer significant implications to us living in a world where an increasing number of people are connected to each other through social networking. We also find that network structures with some intermediate randomness create an interesting scenario in which several norms emerge in a cyclic manner.