A Centipede for Intransitive Preferrers

Clearly, if the agent is myopic, he will do badly in this decision problem: he will refuse the first exchange, which immediately stops the whole sequence. This means that the myopic agent will forgo a sure benefit of 3ε. His behaviour will be self-defeating. If the agent is resolute (cf. McClennen 1990 and 1997), each of the four possible outcomes is available to him. He can simply choose one of them and then go for it. Even though his pairwise preferences are cyclical, he may well have definite views as to which of these four outcomes are choiceworthy. It seems clear that outcome a will not be one of them. It is also quite possible that a +3ε will be be seen by him as choiceworthy. Therefore, it is quite possible that the resolute agent will make the three exchanges. Now, what