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.