Fighting collusion: An implementation theory approach

A competition authority has an objective, which specifies what output profile firms need to produce as a function of production costs. These costs change over time and are only known by the firms. The objective is implementable if inequilibrium, the firms cannot collude on their reports to the competition authority.Assuming that the firms can only report prices and quantities, we characterize what objectives are one-shot and repeatedly implementable.We use this characterization to identify conditions when the competitive output is implementable. We extend the analysis to the cases when a buyer also knows the private information of firms and when the firms can supply hard evidence about their costs.