There are Fixed Price Incentive (FPI) contracts that try to address this. Instead of a single price for the contract as in an Firm Fixed Price (FFP) there is a

There are Fixed Price Incentive (FPI) contracts that try to address this. Instead of a single price for the contract as in an Firm Fixed Price (FFP) there is a "target" price at which the contractor will get some level of profit. Above that you set a cap on the total cost of a project that you are willing to pay, but the profit of the company goes down as you approach the cost cap. So contractors still have the incentive to minimize cost because if they get cost below the "target" price the contractor still gets that as profit. However, people aren't usually a fan of them because it requires all of the overhead/audits of a cost-plus contract which typically minimizes how cost effective they can actually be at getting below the target price. There are also some development-type projects where the government will fund a project, but still require some amount of funds (like 25%) to come from the contractor. But this is really early development type stuff. Basically it is a way to influence where a company is spending their R&D money. Its not really for any operational systems.