We study experimentally cooperation in group contests under a new sharing rule that captures elements of coopetitive setups that are often characterized by the tension between cooperation and competition. It introduces an allocation of the obtained prize which is inversely proportional to individual efforts. We use it to study if the pervasive over-expenditure observed in group contests remains even when individual effort is extremely disincentivized and compare its effects with the egalitarian sharing rule. Participants in our experiment make more effort with the egalitarian than with the inverse proportional rule, but we document a sizeable over-expenditure even with the inverse proportional rule. We find that contribution in a public goods game is positively associated with effort in the group contest. Social value orientation, risk attitudes, competitiveness, or other personality traits do not predict behavior consistently.