Axioms are reviewed for group contest success functions for general production functions, focusing particularly on the additive production function and the multiplicative Cobb-Douglas production function. With one minor exception, these axioms already exist in the literature. This article clarifies which axioms apply and how they apply for group contest success functions. Essential for axioms satisfied by the additive production function, driven by substitutability across efforts, is the sufficiency of only one group member exerting effort. Essential for axioms satisfied by the multiplicative production function, driven by complementarity across efforts, is that all group members exert efforts. The additive production function satisfies an axiom where adding an amount to one effort and subtracting the same amount from a second equivalent substitutable effort does not change the winning probabilities. The Cobb-Douglas production function satisfies a strong homogeneity axiom where an equiproportionate change in matched group member efforts does not affect the winning probabilities.