Efficiency dynamics on scale-free networks with tunable degree exponent

Efficiency dynamics on two coupled small-world networks

“…The contributions to the time evolution of h(t) come from three parts: increase due to learning from its linked agents, increase due to innovation, and decrease due to unforeseen problems. Thus, the growth rate ν of the average efficiency can be expressed as [23][24][25]…”

“…The evolution of the efficiencies is the one used by S.-Y. Huang et al [24] and Z.-G. Shao et al [25], which may mimic the dynamics of efficiencies of competing agents such as airlines, travel, agencies, insurance companies and so on. Our efficiency model on the two coupled small-world networks can be described as follows: Each vertex i in the network represents an agent, which is characterized by a nonnegative integer number h i (t).…”

“…The interactions between the agents are expressed by the networks. The calculated results for present model are independent of the initial conditions [23][24][25]. For simplicity, we set the efficiency of each agent as h i (t) = 0 in the initial conditions.…”

“…Monte Carlo (MC) simulations have been used to study the evolution of the efficiencies of N agents in the small-world network. At each MC step, an agent i is selected at random and its efficient level is updating according to rules [24,25]:…”

“…In the past, a simple model which describes the dynamics of efficiencies of competing agents [23] was developed on a small-world network and on scale-free networks with the tunable degree exponents [24,25]. In this model communications among agents lead to the increase of efficiencies of underachievers, and the efficiency of each agent can increase or decrease irrespective of other agents.…”