Risk–reward share allocation under different integrated project delivery relational structures: A monte-carlo simulation and cooperative game theoretic solutions approach

Sharing of risks and rewards is considered to be one of the key benefits and principles of integrated project delivery (IPD). Despite its importance, risk–reward strategies are not implemented widely in IPD construction projects due to the lack of a well-defined basis for establishing adequate allocation plans. This paper fills this knowledge gap. This research followed a multistep methodology. First, the authors calculated the risk control valuations of all potential combinations of coalitions for IPD stakeholders. This was performed using interrelated steps of risk identification and quantification, risk assignment based on associated contractual analysis, establishment of a coordination network, and Monte Carlo simulation. Second, the authors adopted cooperative game theoretic solutions—including Shapely, Owen, and Myerson partition-graph restricted game values—to allocate risk–reward shares for three IPD relational structures. Third, for each IPD relational structure, the authors evaluated the stability and associated negotiation power of coalitions for the IPD stakeholders using the propensity-to-disrupt ratio. Ultimately, the outcomes of this study show that having a multiparty agreement, in which all stakeholders—the owner, designer, contractor, and subcontractor—have open communication channels, creates the most balanced coalition. In this case, all stakeholders have equal willingness to cooperate in the project. Furthermore, as the engagement of the subcontractor in the IPD coalition decreases, the liability and contribution of the contractor increase in terms of project risk control. The latter emphasizes the importance of the technical capabilities of the contractor in the case of restricted subcontractor’s engagement in the project. This research contributes to the body of knowledge by offering a basis for negotiation among various IPD stakeholders in terms of the degree of the subcontractor’s engagement on the one hand and the proportionate share of each stakeholder on the other hand.