Collaboratively-developed vaccine pricing and stable profit sharing mechanisms

Within the private pediatric vaccine market, we consider the problem of pricing a polyvalent vaccine developed via collaboration between manufacturers that otherwise compete for market share. This study is motivated by the joint development by Merck and Sanofi Pasteur of a hexavalent pediatric vaccine that is undergoing clinical trials for childhood immunizations in the United States. Adopting a cooperative game theoretic framework, we formulate a mixed-integer linear program and a bilevel mixed-integer nonlinear program. When solved sequentially, these mathematical programming formulations identify whether the collaborative venture begets a stable coalition of manufacturers and, if such is the case, a price for the new vaccine that maximizes the net increase in profits among the collaborating manufacturers, subject to the actions of a rational customer seeking to minimize the cost of meeting the Recommended Childhood Immunization Schedule using pediatric vaccines available in the private sector market. We consider a set of profit sharing mechanisms and demonstrate that a convex combination of a subset of the mechanisms assures financial incentive for all participants. Finally, we demonstrate the formulations and price sharing mechanism for the aforementioned hexavalent vaccine in the context of the contemporary United States pediatric vaccine market.