In this paper we consider the problem of scheduling on com- puting platforms composed of several independent organizations, known as the Multi-Organization Scheduling Problem (MOSP). Each organiza- tion provides both resources and tasks and follows its own objectives. We are interested in the best way to minimize the makespan on the entire platform when the organizations behave in a selfish way. We study the complexity of the MOSP problem with two different local objectives – makespan and average completion time – and show that MOSP is NP-Hard in both cases. We formally define a selfishness notion, by means of restrictions on the schedules. We prove that selfish behavior imposes a lower bound of 2 on the approximation ratio for the global makespan. We present various approximation algorithms of ratio 2 which validate selfishness restrictions. These algorithms are experimentally evaluated through simulation, exhibiting good average performances.