As I daresay EF realizes, you can for any "one dimensional k-fold repeated game" solve by means of a recurrence where at each stage, the payoffs for the game are got from the solution to the next stage. [It also is possible to do this in more that one dimension, such as 2D array of games where after each game we move either North or East; this still is polynomial time to solve in any fixed dimension...] It might be interesting to write down the recurrences one can thus get: see if any are interesting+nice as recurrences and try to cook things up to get the simplest and most interesting recurrences you can. It seems to me EF's kind of scenario does arise in real life. Let me give some examples. In a multigame chess match (first to win 10 games win match). Each game you have option of playing a double-edged opening like sicilian defense, or a safer opening more likely to yield a draw. That choice is a meta-game analysable using EF-like approach. I thought in the Anand-Kasparov world champ match Anand was mis-playing this meta-game -- not that I'm really capable of disputing players of their calibre. In an american football game, again, each "down" is like an individual game and total yardage is like EF's points so far. In politics, Scum runs for the presidency versus Twit. Each week, another poll indicates who's currently ahead and each must decide what move to make that week, such as hacking the other guy's web site, making another incredibly stupid TV ad lying about opponent featuring mega-edited video, getting wife to come testify to cameras that you'd never betray her, arranging that voter registrations will be rejected in some state if they are not written on unavailable ultra-thick paper, etc. Some of these moves are riskier but have potentially higher payoff than others. Again, this is an iterated-game. -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)