Nowadays many economic fields are dependent on information flows. Information serves as a strategic tool in economics, business and many social processes. In particular, spreading information among taxpayers can be used as a control parameter in tax control. The probability of auditing which encourages tax payments used to be considered as a unique tool to stimulate tax collection. The current study represents a combined approach where tools of evolutionary game theory and network modeling are applied to the analysis of agents’ economic behavior. Information of possible tax auditing is disseminated across the population of taxpayers and is supposed to be a main factor influencing their decision on whether to evade or not. According to the previous research, interactions and dissemination of information or rumors among taxpayers in long-term period can be formulated as an evolutionary process. It is assumed that agents tend to spread information or rumors over their own contact network of neighbors and colleagues rather than over randomly chosen agents. Thus, the network model of social interaction is constructed. Information spreading in the network of various topology (e.g. grid, random network, etc.) is considered as an evolutionary process where agents’ behavior is described by the stochastic imitation dynamics and their interaction is described by different modifications of the bimatrix games which generate evolutionary dynamics. Scenario analysis is supported by the series of experiments. Numerous simulations help visualize the process of information spreading across different types of network, imitation protocols and players payoffs. The results show that information flow helps encourage tax payments in the population.