Obviously strategyproof mechanisms without money for scheduling

We consider the scheduling problem when no payments are allowed and the machines are bound by their declarations. We are interested in a stronger notion of truthfulness termed obvious strategyproof-ness (OSP) and explore its possibilities and its limitations. OSP formalizes the concept of truthfulness for agents/machines with a certain kind of bounded rationality, by making an agent's incentives to act truthfully obvious in some sense: Roughly speaking, the worst possible outcome after selecting her true type is at least as good as the best possible outcome after misreporting her type. Under the weaker constraint of truthfulness, Koutsoupias [2011] proves a tight approximation ratio of for one task. We wish to examine how this guarantee is affected by the strengthening of the incentive compatibility constraint. The main message of our work is that there is essentially no worsening of the approximation guarantee corresponding to the significant strengthening of the guarantee of incentive-compatibility from truthfulness to OSP. To achieve this, we introduce the notion of strict monitoring and prove that such a monitoring framework is essential, thus providing a complete picture of OSP with monitoring in the context of scheduling a task without money.