In this chapter we give a very brief overview of some fundamentals from mechanism design, the branch of game theory dealing with designing protocols to cope with agents' private incentives and selfish behavior. We also present recent results involving a new, extended utilities model that can incorporate externalities, such as malicious and spiteful behavior of the participating players. A new notion of strong truthfulness is proposed and analyzed. It is based on the principle of punishing players that lie. Due to this, strongly truthful mechanisms can serve as subcomponents in bigger mechanism protocols in order to boost truthfulness. The related solution concept equilibria are discussed and the power of the decomposability scheme is demonstrated by an application in the case of the well-known mechanism design problem of scheduling tasks to machines for minimizing the makespan.