The paper deals with a detailed analysis of a game theory-based vehicle-pedestrian interaction model adopted from literature. For the sake of simplicity only single-vehicle/single-pedestrian model is considered. The adopted model is extended with a stochastic component that accounts for variability in pedestrian/driver behaviors and influence of multi-agent environment. The model is generalized for scenarios where pedestrian appears at different distances relative to crosswalk. The analysis study is organized as follows. First, an off-line analysis of model-derived probability distributions and corresponding crossing decisions is conducted to gain initial insights. Next, large-scale simulations of the model are conducted for a wide set of randomly generated initial conditions and stochastic component tunings. Finally, the obtained simulation results are analyzed and discussed.