Bayesian Game Analysis for Risk-Sharing Effectiveness of Price Adjustment Clauses in Transportation Projects

Abstract

Departments of transportation commonly adopt trigger-based price adjustment clauses (PACs) to share risks of volatile material prices. Although existing research found no statistical evidence that the inclusion of PACs lowers contractors’ bids, qualitative studies have revealed that stakeholders continue to perceive PACs as beneficial. This leaves PACs’ ability to achieve a true risk-sharing equilibrium unresolved. As such, there is a dire need for a systematic investigation of PACs incorporating market volatility, project durations, and contractor bidding and behavioral strategies. This paper evaluates the effectiveness of PACs in facilitating equitable risk-sharing under varying market scenarios and project timelines. A comprehensive three-step approach is adopted through (1) retrieving and analyzing historical price data to capture prevailing trends; (2) using a Bayesian Nash equilibrium under game theory across 324 project scenarios to derive optimal strategic insights; and (3) applying decision tree classification to generalize the findings. Findings indicated that when prices experience a significant inflation throughout the project’s lifetime, a DOT’s best strategy is to apply high trigger values. However, there is a lack of equilibrium under such high trigger values because the results show that the contractors’ best strategy is to overbid. The same equilibrium status for contractors (i.e., overbidding) manifests in balanced market conditions. To this end, DOTs can better manage this by setting average trigger values and implementing performance-based incentives. When prices decline, scenarios suggest that retaining PACs while eliminating trigger values has proven most effective toward equilibrium. This study challenges the assumption that PACs foster equitable risk-sharing, advocating instead for data-driven, dynamic approaches that reflect real-time market behavior rather than static thresholds.