Take a look at Stickk's business model (https://www.stickk.com/tour). Consider an example of the game that your current self would be playing with your future self when you come up with a new year's resolution. Suppose your current self (The Planner) may choose between putting something at stake or not. (S)he will derive some positive happiness utility (of +100) if you achieve your goal but has to incur a small annoyance (-20) of putting something at stake. Your future self (The Procrastinator) may choose between taking action towards your goal or doing something else. Taking action is annoying (costs -20) and (s)he will derive happiness utility of (+100) from doing something else. However, if (s)he does something else and there is something at stake, (s)he will derive utility x.. Are there any equilibria in pure strategies