Supplement to "Timing and Self Control"

This appendix has several sections. W1 is another example/application of the model.  W2 is a brief proof of something asserted in the text. W3 provides a foundation for the model in terms of a game between the long run self and a sequence of shorter one selves. W4 explores an alternative model; it shows that the alternative makes no difference with linear control sets but leads to odd conclusions when the cost is convex.