Prize sharing in collective contests

The characteristics of endogenously determined sharing rules and the group-size paradox are studied in a model of group contest with the following features: (i) The prize has mixed privatepublic good characteristics. (ii) Groups can differ in marginal cost of effort and their membership size. (iii) In each group the members decide how much effort to put without observing the sharing rules of the other groups. We provide simple characterizations of the relationship between group characteristics, performance of the competing groups (winning probability and per capita expected utility) and the type of sharing rules they select. Interestingly, richer and more efficient groups or groups with larger valuation of the prize tend to be more equalitarian. We also clarify under what circumstances such tendency is due to larger membership.