Hierarchy and the size of a firm

In this note, we apply weighted hierarchical games of cooperative game theory to the problem of optimal firm size of the firm. In particular, we analyze the influence of production technology on the size of the firm. Our note enhances previous approaches using a permission structure with equally strong relationships between predecessor and direct successors.

A Study on Profit Distribution for Water Rights Cooperation Taking into Account Dominant Power of Transfer Sectors

In this paper, we explore the issue of profit distribution for water resources collaborative alliances that are composed of one single water rights transfer sector and several water resources requirement sectors. Considering the dominant position of the water rights transfer sector in water resources cooperation, we propose a novel 3-step approach on profit distribution for coalitions by applying game theory for interactions that include coalition structures and permission structures. We examine the effectiveness of this approach by a case study of water rights cooperation between the agriculture sector and agroindustrial sectors of the Karoon river basin in Iran. The results show that this approach allows players who have veto rights to obtain more payoffs from the coalition’s profit distribution in contrast to using the Owen value. In other words, the distribution results of the 3-step approach reflect the advantage held by the water rights transfer sector based on its veto power. Further, our proposed 3-step approach takes the permission structure among a priori unions into consideration when distributing the profits of the water resources coalition while the P-Owen value considers only the permission structure among players.