It is well known that Peterson’s algorithm for two processes is starvation free. In this talk I study the generalization of Peterson’s algorithm to N>2 processes using tournament trees. In particular, I will show how, contrary to the two processes version, this algorithm is not starvation free if we do not make any fairness assumptions. To overcome this issue, I propose a new variation of the algorithm that enforces starvation freedom and bounded overtaking without imposing any fairness assumption.