This paper proposes a methodology to study what ordering strategy will be chosen by companies in a supply chain when risk is taken into account. Here, risks are measured as the standard deviation of the customer service and on-hand inventory levels induced by the three considered strategies. We apply this methodology to investigate the conditions under which optimisation-based and stream management-based strategies are preferred. We find that the considered traditional optimisation-based strategy appears more often in Nash equilibria than any of our two stream management-based strategies. To our knowledge, the methodology itself is one of the first to demonstrate how to take several constraints (market demand, and preferences of companies over customer service and inventory levels) into account when choosing an ordering strategy.