How does an individual move through a crowded environment, and how do local rules shape its large-scale motion? Lattice gases offer a powerful framework to address this question: particles perform random walks on a lattice with hardcore exclusion, and a driven tracer particle probes how the environment affects transport, through its velocity and diffusivity as functions of the density of obstacles. In many real situations, however, pure exclusion is unrealistic: it is often easier to move through a crowd by pushing obstacles out of the way. In this internship, we will study a "pushy" tracer that can displace the particles blocking its path, a mechanism that has received almost no attention so far. Combining numerical simulations and analytical methods (master equation, high- and low-density expansions), the student will determine how pushing modifies the speed and diffusivity of the tracer, and characterize the environment seen from its moving frame. Is it worth being a bully?