Royalty bargaining in Public–Private Partnership projects: Insights from a theoretic three-stage game auction model

•It is a transformed first-price sealed-bid auction with independent private values.•We consider interactions between bidding and bargaining behaviors in a franchise.•The true values bidders assign to a project influence royalties and subsidies.•The payoff of a government from outside options affects royalties and subsidies.•The payoff of a government from outside options is vulnerable to collusion.

This study presents a transformed first-price sealed-bid auction with independent private values to determine the equilibrium royalties and subsidies in Public–Private Partnerships. The proposed model implies that royalties and subsidies are influenced by the true values bidders assign to a target project and the payoff received by a government from taking up its outside options instead of its bargaining power. In addition, such payoff is vulnerable to collusion. A real case is also detailed to show how reported signals, royalties and subsidies are determined in different cases.