Mixed sharing rules

It is wellknown that a group of individuals contributing to a joint production process with diminishing returns will tend, in equilibrium, to put in too little effort if shares of the output are exogenous, and will put in too much effort if their shares are proportional to their inputs. We consider 'mixed' sharing rules, in which some proportion of the output will be shared exogenously, and the rest proportionally. We examine the efficiency properties of such rules, compare them with serial sharing rules, and suggest a sharing game whose noncooperative equilibrium is, in certain circumstances, Pareto efficient