A polluted river network is populated with agents (e.g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network....

We establish a new envelope theorem in which the choice variables are discrete and the objective function and the constraints are Lipschitz continuous with respect to the parameters. The parameters can be ?nite or in?nite dimensional vectors in a Banach space. In an application, we revisit the...

This paper considers a trading problem on a network with incomplete information. We consider a simple water trading problem in which three agents are located in a linear order along a river. Upper stream agents can sell some amount of the water to their downstream but not the other way around....

We consider the cost sharing problem with divisible demands of heterogeneous goods. We propose a cost sharing method called Proportionally Adjusted Marginal Pricing (PAMP) method. PAMP is a nonadditive (in the cost function) extension of average cost pricing. We introduce an axiom called Local...

For a tolled highway where consecutive segments allow vehicles to enter and exit unrestrictedly, we propose a simple toll pricing method. It is shown that the method is the unique method satisfying the classical axioms of Additivity and Dummy in the cost sharing literature, and the axioms of...