The head-on collision between electrostatic shocks is studied via multi-dimensional Particle-In-Cell simulations. A strong magnetic field develops after the interaction, which causes the shock velocities to drop significantly. This transverse magnetic field is generated by the Weibel instability, which is driven by pressure anisotropies due to longitudinal electron heating while the shocks approach each other. The possibility to explore the physics underpinning the shock collision in the laboratory with current laser facilities is discussed.