Should game theoretic paradoxes invalidate an ethical theory?
Utilitarianism operates under the rule "perform the action which maximises utility overall".
Proposition: Retaliation violates utilitarianism because actions don't affect the past so utilitarianism implies that only future utility should be considered.
Suppose someone always adhered to utilitarianism and then suppose that there is some hostile party who knew this and could exploit it for their own gain in a way that promoted utility for them but reduced it overall for everyone. The only way circumstances like this could be prevented is by the utilitarian adopting a policy of always retaliating against exploitation of this nature to act as a deterrent. If holding such a policy increased utility overall then it would be in accordance with utilitarianism. However, if they hold this policy then implementing it would violate the proposition if the retaliation held no other purpose then in carrying out the policy.
Thus both holding and not holding the policy lead to violations of utilitarianism so this theory is inconsistent. The only way to resolve it is to deny the proposition which would itself deny the linear nature of time.