Abstract:

Bipartite rationing problem was studied to divide a short supply between resource and sink nodes in a bipartite graph. It had been used to deal with numerous issues in the real world, such as, the allocations of aid relief during natural disasters, utilities like electricity and natural gas, and talents of different types to universities, etc. From the view of marginal contribution of coalitions, this paper proposed the Shapley solution of bipartite rationing problems calculated by linear programming, and characterized it by cooperative game and axiomatization. First, we defined the cooperative game of bipartite rationing problems, called the bipartite rationing game, and proved that the Shapley value of the corresponding cooperative game coincides with the solution we propose. Then, we showed that the Shapley solution is the unique feasible allocation satisfying priority-consistency. Finally, we considered the application of the Shapley solution to museum pass problems, and discussed the allocations of the revenue of single tickets and pass tickets of each participating museum.

Key words: bipartite rationing problem, cooperative game, Shapley value, axiomatization, museum pass problem