Testing Truthfulness for Single Parameter Agents

We consider the task of designing truthful mechanisms for single parameter agents. We prove a general sufficient condition for truthfulness when the valuation function of the agents of any outcome is one dimensional and continuous. For certain types of natural valuation functions, our condition is also necessary. One of the main advantages of our characterization is that it provides a computationally efficient method for testing whether a given algorithm admits a truthful payment scheme. We then demonstrate the simplicity of testing our condition by showing that classical criteria for truthfulness in combinatorial problems such as auctions and machine scheduling can be derived from our condition. In addition, we use our condition to derive results for new single parameter problems, which have not been previously analyzed.We also consider combinatorial problems where the true types of agents affect the valuation of each other, such as in load balancing. In such cases there are no efficient dominant strategy mechanisms. We show that the same condition can be used to design mechanisms which are ex-post truthful, meaning that the outcome where all agents cooperate and report their true type is a Nash equilibrium. We demonstrate the power of this condition by applying it on the problem of machine scheduling with strategic job owners, which was not addressed before. We prove upper and lower bounds for ex-post truthful mechanisms for this problem.