On the complexity of exchanging

•We analyse the computational complexity of the trade robustness problem.•We look at the problem of turning winning coalitions into losing coalitions.•We consider the trade robustness problem for different representations.•We give remaining problems related with trade robustness.

We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.