Axiomatizing multi-prize nested lottery contests: A complete and strict ranking perspective

Multiple prizes are usually awarded in contests (e.g., internal promotions, school admissions, sports, etc.) and players exert effort to increase their chances for winning a higher prize. A multi-prize contest model must provide each player's probabilities of winning each prize as functions of all players’ efforts. We find that the key notion of “hypothetical subcontests” in the contest axiomatization literature initiated by Skaperdas (1996) can be appropriately interpreted and precisely defined from a ranking perspective, as well as the relevant axioms of “Subcontest Consistency” and “Independence of Irrelevant Contestants” (IIC). When there are less than four contestants (exclusive), a set of axioms properly adapted from those in Skaperdas (1996) and Clark and Riis (1998a) are sufficient and necessary for axiomatizing the widely adopted multi-prize nested lottery contest of Clark and Riis (1996a). When there are more than four contestants (inclusive), including a new axiom of “Independence of Irrelevant Ranks” (IIR) is necessary and sufficient.