Firm X can produce a necessary component in-house at a cost of 10 or purchase it from one of three suppliers (A, B, or C) whose costs are 8, 7, and 5, respectively. X can approach the firms in any order, attempt to negotiate an agreement with the first, and, if this fails, go on to the second, and so on. There is no cost to approaching a new firm, but X can negotiate with each firm only once. In any negotiation, the firms will split equally the available total profit (if any). Here total profit is measured relative to each side’s next-best alternative; for X, this alternative is a deal with any supplier not yet tried.
Show that X’s optimal strategy is to approach C first, then B, then A, if necessary. Do X and C reach an agreement? At what price? What do your answers suggest about the benefits of competition?