The long-run is about what happens in the limit, or eventually, or in the infinite case. Think convergence of a sequence, common knowledge, repeated games, computing the value of a function for any argument, betting often. The short-run is about what happens now, or by time t, or in a particular case. Think this term of a sequence, mutual knowledge, one-off games, computing the value of a function for that argument, betting once.
Sometimes the long-run is taken to be irrelevant to the short-run ("in the long run we're all dead"); and sometimes it's not. When? Why? How?
This is a collection of notebooks related to the long-run and the short-run. The main notebook is "the long-run and the short-run". That describes the issue in general, and uses long-run justifications of decision rules as a case study. The others expand on bits and pieces from that. For example, "laws of large numbers" is a non-technical explanation of the Weak and Strong Laws of Large Numbers; "population growth" describes a simple model of population growth in a variable environment, and its relation to Kelly betting; "how to iterate a gambling problem" precisifies the conjecture that long-run justifications of decision rules are cheap, and so don't show much.
Because seeing is believing, the notebooks make use of interactive simulations. You can play around with these using Binder. Launch it by clicking the Binder badge below.
