Bargaining on Price on Behalf of Price-Insensitive Downstream Consumers

There are settings in which linear prices are negotiated by procurement agents and final consumption decision made by end users who are indifferent to negotiated prices.For example, a patient seeking medical treatment is indifferent to the treatment's cost, if it is covered by his insurance program. We study bargaining for per-unit prices between suppliers and an intermediary who represents price-insensitive consumers. Under simultaneous bargaining with all suppliers, the resulting prices exceed the value of the good (or service) being delivered, provided that the suppliers have sufficiently large bargaining power. This overpricing is solved if simultaneous negotiations are replaced by sequential ones. The problem with sequential negotiations is that they necessitate treating the suppliers asymmetrically, even if they are symmetric. We utilize the result about sequential negotiations as a building block in a multi-period model that resolves the issue: in this model, overpricing is prevented and all suppliers are treated the same