looking for a game engine

Hi I am looking for a simple game engine I could use to show students how to developp a game. The basic features of this engine would be : - 3d directX/openGL support - network IPX support - collision detection - object support : the players would pick up objects just by walking on them - inventory 2D layer - hardware input support : mouse, joystick, VR headsets This would be a simple labyrinth treasure hunt game where the players would have to find a treasure the first. They could use objects they would have picked up : - to unlock doors - to put traps for the other players : releasing some special objects would trigger them and open traps such as temporary walls or holes Do you know some free game engine I could use for this demonstration please ? thanks Cyril