A contest success function for rankings

• DOI: 10.1007/s00355-016-0997-5
• Publication Date: 2016-09-27T10:43:00Z
• Authors: Alberto Vesperoni
• Keywords: jel:C70; jel:D81; 330; jel:D74; 0502 economics and business; 05 social sciences; jel:D72; conflict; contest; ranking; success function; axiom; probabilistic choice; jel:C25

In a contest, several candidates compete for winning prizes by expending costly efforts. We assume that the outcome of a contest is a ranking, which is an ordered partition of the set of candidates. We consider rankings of any type (i.e., with any number of candidates at each rank), and define a class of success functions that assign probabilities to all rankings of a given type for each configuration of candidates’ efforts. Our framework can be interpreted as the probabilistic choice of a committee that allocates a given set of prizes following a mix of objective and subjective criteria, where the former depend on candidates’ efforts while the latter are random. We axiomatically characterize our class of success functions and illustrate its relevant features to contest games.