Infinite past

`At every day a player takes an action’. This is the starting point of many models of repeated interaction. We let time run to infinity to reflect the fact that players don’t have in mind a fixed termination point for the game. We do, however, fix the starting point , which I think in many cases is unnatural: By the time I realize I know the bartender in my local Starbucks and maybe I should start tipping, I already lost count of the number of times I have been there. This is why I would like to model it as a game with infinite past. Also, it will be cool to have a paper that starts with `At every day ‘ for a change. But, as I am sure many game theorists have independently discovered, it is not clear how to proceed.