An agent with intransitive preferences who is willing to make exchanges can be exploited without limit.

The barebones theory of rationality discussed above in Section 1.1 takes an agent’s preferences (rankings of states of affairs) to be rational if they are complete and transitive, and it takes the agent’s choice to be rational if the agent does not prefer any feasible alternative to the one he or she chooses. Such a theory of rationality is clearly too weak, because it says nothing about belief or what rationality implies when agents do not know (with certainty) everything relevant to their