An axiomatization of difference-form contest success funcions [WP]

Abstract

This paper presents an axiomatic characterization of difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. This axiomatization rests on the property of Absolute Consistency, stating that the difference in winning probabilities between two contenders in the grand contest must be the same as when they engage in smaller contests. This property overcomes some of the drawbacks of the widely-used ratio-form contest success functions. Our characterization shows that the criticisms commonly-held against difference-form contests success functions, such as lack of scale invariance, are unfounded. Finally, we extend our axiomatization to relative-difference contests where winning probabilities depend on the difference of contenders effective efforts relative to total aggregate effort.