Definition of Cost Sharing and Matching. Cost sharing is a phrase used to indicate that more than one sponsor will share in the costs associated with a project. The most common relationship is for an external sponsor to provide most of the funds and for the University to provide the remainder of the project funds. Matching is a form of cost sharing that generally defines a specific ratio of sponsor and University dollars. This type of cost share is usually an eligibility requirement stated in the RFP (Request for Proposal) and is most often provided from institutional resources.