Reducing Bayesian Mechanism Design to Algorithm Design

The goal is to design algorithms that succeed in models where input is reported by strategic agents (henceforth referred to as strategic input), as opposed to standard models where the input is directly given (henceforth referred to as honest input). For example, consider a resource allocation problem where a single user has m jobs to process on n self-interested machines. Each machine i can process job j in time tij , and this is privately known only to the machine. Each machine reports some processing times O tij to the user, who then runs some algorithm to determine where to process the jobs. Good approximation algorithms are known when machines are honest (i.e., O tij D tij for all i; j ) if the user’s goal is to minimize the makespan, the time elapsed until all jobs are completed, going back to seminal work of Lenstra, Shmoys, and Tardos [13]. However, such algorithms do not account for the strategic nature of the machines, which may want to minimize their own work: why would they report honestly their processing time for each job if they can elicit a more favorable schedule by lying? To accommodate such challenges, new algorithmic tools must be developed that draw inspiration from Game Theory. Requiring solutions that are robust against potential strategic manipulation potentially increases the computational difficulty of whatever problem is at hand. The discussed works provide a framework with which to design such solutions (henceforth called mechanisms) and address the following important question.