Cooperation among unrelated individuals in social-dilemma-type situations is a key topic in social and biological sciences. It has been shown that, without suitable mechanisms, high levels of cooperation/contributions in repeated public goods games are not stable in the long run. Reputation, as a driver of indirect reciprocity, is often proposed as a mechanism that leads to cooperation. A simple and prominent reputation dynamic function through scoring: contributing behaviour increases one's score, non-contributing reduces it. Indeed, many experiments have established that scoring can sustain cooperation in two-player prisoner's dilemmas and donation games. However, these prior studies focused on pairwise interactions, with no experiment studying reputation mechanisms in more general group interactions. In this paper, we focus on groups and scores, proposing and testing several scoring rules that could apply to multi-player prisoners' dilemmas played in groups, which we test in a laboratory experiment. Results are unambiguously negative: we observe a steady decline of cooperation for every tested scoring mechanism. All scoring systems suffer from it in much the same way. We conclude that the positive results obtained by scoring in pairwise interactions do not apply to multi-player prisoner's dilemmas, and that alternative mechanisms are needed.