This paper presents an analysis of social dilemmas that arise when passengers are faced with choosing between personal vehicles and buses in a mixed traffic flow. We conducted the computer simulation using a cellular automata framework to analyze the case. The Revised S-NFS model describes the dynamics of vehicles in a single lane, while Kukida's model defines the rules for lane changing. The presence of social dilemma is determined by the social efficiency deficit. We selected four scenarios that represent different states on the fundamental diagram of personal vehicle flow: free flow, critical point, congested flow, and heavy congested flow. The simulations were performed on an infinite two-lane road. The results show that a social dilemma of the prisoner type exists in congested and heavy congested flow, but not in free flow. Additionally, we have conducted a simulation for the scenario with a dedicated bus lane. This simulation has shown the presence of the chicken-type social dilemma. Simulation results can enhance our comprehension of choosing transportation modes.