Coalition-proof payment plan in delegation of design verification in public works

This paper considers three-tier hierarchy including a principal who delegates both a design of public work and its verification work, an agent to whom a principal delegates the design work, and an inspector to whom a principal delegates the design verification. This paper includes two types of coalitions; one is that an agent offers a bribe to an inspector to abstain from checking the design drawing, dissatisfying the principal´s performance requirement to save the design cost (Type1), and the other is that an agent offers a bribe to an inspector to conceal the verifiable evidence showing inadequate design drawing (Type2). It is shown that Type 1 coalition is more critical for a principal in the case where a principal selects an agent and an inspector simultaneously. In addition, we compared the case where a principal selects an agent and an inspector simultaneously with the one where a principal selects an inspector after an agent produces a design drawing. It is shown that the total payment to an agent and an inspector become lower in the latter case.