This study constructs a royalty negotiation model for the bi-level programming (BLP) problem and develops a heuristic algorithm for solving the BLP problem. Concession rate, learning effect, and the time value discount rate are integrated into the proposed algorithm to reflect an authentic...

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...