Here, we developed 2-dimensional multi agent random walk algorithm. In our algorithm, agents interact with each other and change their directional rules by detecting other agents' moving direction locally. In addition to that, modulation effects in which agents control rule intervals depending on amount of local other agents are equipped to our model. We show that modulation effects which introduce global ambiguity play a crucial role to establish optimal random walk by checking the slope value (μ) depending on dense of agents. We set modulation-added model and non-modulation model. The latter is control model. In case of non-modulation model, the slope values (μ) highly depends on dense of agents. However, in case of modulation-added model, the slope values (μ) are flexible and independent from dense of agents.