There are situations in which competitors ally to pursue a common objective. This simultaneous presence of cooperation and competition is called coopetition and we study it theoretically and experimentally in a group contest setup. More concretely, we analyze a group contest with a new sharing rule, that we call inverse proportional. This rule embodies the idea that the more a member of a group contributes to win the contest, the less this member is able to capture the potential posterior prize, introducing thus a competitive element into group decision-making. We compare the effects of this rule with a standard, the egalitarian sharing rule. While in the egalitarian case theoretically the optimal individual contribution is positive, with the inverse proportional rule zero contribution represents the individual (and also the social) optimum. We find that participants in our experiment contribute more with the egalitarian than with the inverse proportional rule. We also document over-expenditure with the inverse proportional sharing rule, suggesting that group contest generates inefficient behavior even when individuals are extremely penalized for their contributions. We also explore the drivers of decision in the group contest, and find that contribution in a public goods game is positively associated with contribution in the group contest and that competitiveness explains part of the behavior with the inverse proportional rule but not with the egalitarian sharing. Neither social value orientation, risk attitudes, nor personal traits appear as significant predictors of behavior.