Profit-sharing and efficient time allocation

Agents are endowed with time, which in turn is invested in projects that generate profit. A mechanism divides the profit generated by these agents depending on the allocation of time as well as the amount of profit made by every project. We study mechanisms that incentivize agents to contribute their time to a level that results in the maximal aggregate profit at the Nash equilibrium, regardless of the production functions involved (efficiency). Our main finding involves the characterization of all mechanisms that satisfy efficiency. Furthermore, within this class, we characterize the mechanisms that are monotone on the addition of time to agents as well as those monotone on the payoffs of the agents with respect to technological improvements in the generation of profit. The class of efficient mechanisms depends on the type of available projects and their connectedness. It expands earlier profit-sharing mechanisms that are independent of profit generation.