A game-theoretic assessment of urban road-network vulnerability: a case study of Naples, Italy

Urban road-network vulnerability is difficult to assess when disruption probabilities are unknown and alternative paths perform differently under adverse network conditions. This study proposes a game-theoretic framework in which network users and an adversarial entity interact through a two-player non-cooperative zero-sum game. Users minimize expected travel cost by selecting mixed strategies over alternative paths, while the adversarial entity maximizes it by selecting mixed strategies over predefined disruption scenarios. The framework integrates alternative-path generation, scenario-specific travel costs from PTV VISUM, and linear programming to determine minimax equilibrium strategies. An application to 25 selected origin-destination pairs in the metropolitan road network of Naples, Italy, considers five road-closure scenarios and evaluates both physical disruption exposure and strategic importance. The results show that the disruption affecting the largest number of paths does not necessarily exert the greatest strategic influence on the equilibrium. Mixed user strategies emerge for 20 of the 25 origin-destination pairs and reduce worst-case travel cost relative to the best pure-path worst-case benchmark. Demand-weighted results further confirm that physical exposure and strategic importance provide distinct information on network vulnerability. From a practical perspective, the framework can support transport planners in distinguishing disruptions with broad physical impacts from those that exert greater strategic influence on path-choice strategies. The proposed framework therefore complements conventional disruption assessment by explicitly accounting for path diversification and strategic interaction without requiring predefined disruption occurrence probabilities.