Co-opetition in enhancing global port network resiliency: A multi-leader, common-follower game theoretic approach

•Formulation and solution of co-opetitive, multi-port protective investment problem.•Considers market interactions, disaster/investment impacts, cooperation, competition.•Conceptualized as multi-leader (ports), common-follower (liner shipping network) game.•Formulated as an Equilibrium Problem with Equilibrium Constraints (EPEC).•Co-opetition supports greater overall throughput and reduced network shipping costs. Ports are key elements of global supply chains, providing connection between land- and maritime-based transportation modes. They operate in cooperative, but competitive, co-opetitive, environments wherein individual port throughput is linked through an underlying transshipment network. Short-term port performance and long-term market share can be significantly impacted by a disaster event; thus, ports plan to invest in capacity expansion and protective measures to increase their reliability or resiliency in times of disruption. To account for the co-opetition among ports, a bi-level multiplayer game theoretic approach is used, wherein each individual port takes protective investment decisions while anticipating the response of the common market-clearing shipping assignment problem in the impacted network. This lower-level assignment is modeled as a cost minimization problem, which allows for consideration of gains and losses from other ports decisions through changes in port and service capacities and port cargo handling times. Linear properties of the lower-level formulation permit reformulation of the individual port bi-level optimization problems as single-level problems by replacing the common lower-level by its equivalent Karush Kuhn Tucker (KKT) conditions. Simultaneous consideration of individual port optimization problems creates a multi-leader, common-follower problem, i.e. an unrestricted game, that is modeled as an Equilibrium Problem with Equilibrium Constraints (EPEC). Equilibria solutions are sought by use of a diagonalization technique. Solutions of unrestricted, semi-restricted and restricted games are analyzed and compared for a hypothetical application from the literature involving ports in East Asia and Europe. The proposed co-opetitive approach was found to lead to increased served total demand, significantly increased market share for many ports and improved services for shippers.