Bargaining on price on behalf of price-insensitive downstream consumers

There are settings in which prices are negotiated by procurement agents and final consumption decisions are 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 the commonly used simultaneous bargaining framework we show that, if suppliers have sufficiently high bargaining power, the resulting prices will exceed the value of the good (or service) being delivered. This overpricing is solved if simultaneous negotiations are replaced by sequential ones. The theoretical problem with sequential negotiations is that they necessitate treating the suppliers asymmetrically, even if they are symmetric; the empirical problem with sequential negotiations is that the negotiations-order is unobservable. We propose a multi-period model that resolves these issues: overpricing is prevented and all suppliers are treated the same. In this model, the result about sequential negotiations is utilized in order to produce (asymmetric) off-path threats. These threats sustain symmetric on-path play.