Pricing Competition Between RoRo Shipping and Road Transport: A Stochastic Nash Equilibrium Approach with Shipper Heterogeneity

Short sea shipping (SSS) faces persistent challenges competing with road transport despite its lower emissions. Roll-on/Roll-off (RoRo) carriers share the same cargo types as road haulage, making pricing competition central to achieving modal shift. Existing stochastic freight models primarily address behavioural uncertainty but overlook operational and market uncertainty, while game-theoretic pricing models typically assume perfect foresight of costs, demand, and preferences. In practice, however, RoRo operators must commit to long-term prices, often through annual contracts, while facing simultaneous uncertainty across all three dimensions. We develop a singlestage stochastic pricing model with long-term price commitments, in which two competing carriers simultaneously choose prices and service frequencies to maximise expected profit. Market and demand uncertainty are represented through a finite set of scenario-based demand and cost regimes with exogenously specified probabilities, capturing different economic environments such as recessions, stable markets, and high-demand conditions. These scenarios reflect uncertainty over aggregate market conditions relevant for long-term freight pricing and operating costs [1,2]. Customer heterogeneity is modelled through profit margin distributions. Low-margin shippers (e.g. bulk commodities and construction materials) exhibit high price sensitivity, as logistics costs may account for up to 30% of total costs, while high-margin shippers (e.g. pharmaceuticals and electronics) are primarily time-sensitive. In equilibrium, each carrier maximises expected profit by jointly choosing prices and service frequency, trading off against demand responses and operating costs, while accounting for the strategic response of the competing mode. Within each scenario, demand is determined by a logit-based choice model. Mixed-logit demand integrals are approximated using Monte Carlo simulation and quadrature-based techniques, and Nash equilibrium prices and service frequencies are computed via iterative best-response cycles. At each iteration, each carrier solves a mixed-integer optimisation model with a linearised representation of demand responses. Computational experiments illustrate how explicitly representing shipper heterogeneity and market uncertainty affects equilibrium pricing outcomes. The results indicate that accounting for behavioural heterogeneity can substantially alter competitive pricing incentives, particularly in markets structurally favourable to road transport, where homogeneous-shipper models tend to exaggerate competitive pressure. Comparisons with scenario-specific deterministic pricing suggest that a single price and frequency decision, applied consistently across scenarios, can perform comparably well on average, supporting the use of a stochastic equilibrium framework for analysing long-term pricing decisions. For operators, the framework clarifies which customer segments remain economically viable under adverse market conditions and provides structured insight into pricing decisions under long-term uncertainty. The scenario-based stochastic equilibrium formulation could be adapted to other intermodal competition settings where tariffs are set before demand conditions are observed.