We describe the GRB and all-sky monitor experiment (GAME) mission submitted by a large international collaboration (Italy, Germany, Czech Republic, Slovenia, Brazil) in response to the 2012 ESA call for a small mission opportunity for a launch in 2017 and presently under further investigation for subsequent opportunities. The general scientific objective is to perform measurements of key importance for GRB science and to provide the wide astrophysical community of an advanced X-ray all-sky monitoring system. The proposed payload was based on silicon drift detectors (~1–50 keV), CdZnTe (CZT) detectors (~15–200 keV) and crystal scintillators in phoswich (NaI/CsI) configuration (~20 keV–20 MeV), three well established technologies, for a total weight of ~250 kg and a required power of ~240 W. Such instrumentation allows a unique, unprecedented and very powerful combination of large field of view (3–4 sr), a broad energy band extending from ~1 keV up to ~20 MeV, an energy resolution as good as ~250 eV in the 1–30 keV energy range, a source location accuracy of ~1 arcmin. The mission profile included a launch (e.g. by Vega) into a low Earth orbit, a baseline sky scanning mode plus pointed observations of regions of particular interest, data transmission to ground via X-band (4.8 Gb/orbit, Alcantara and Malindi ground stations), and prompt transmission of GRB/transient triggers.