Documentation/tutorial on equilibria with unreached information sets

[tturocy]

There are some subtle points that arise when looking at an equilibrium (or more generally a behaviour profile) in which information sets are reached with zero probability. It would likely be useful to improve at least the documentation on this, but also possibly some new concepts are needed. See #660 and #446, for example, for some relevant background.

• We have now (as of Clarify definitions of behaviour profile values for unreached information sets #816) decided to follow a convention where several quantities related to values conditional on reaching an information set are returned as nulls for unreached information sets. This is conservative. However, note that it may be possible for an information set to be unreached but yet come of these conditional quantities can only have one value. For example, consider a proper subgame where all nodes in the proper subgame are reachable; there are other examples one can come up with.

• In extensive forms, the natural way to think about sets of equilibria is (arguably) based on the probability distribution they induce over terminal nodes. Very frequently there are sets of equilibria that induce the same distribution, differing only in the actions assigned off the equilibrium path. Our current convention (as of 16.6) is to return a sample equilibrium from such sets, but this is perhaps not as transparent as it could be because it could suggest to calling code that this is the only such equilibrium; advice explaining this is currently only written in text in the documentation as opposed to being modelled formally.

• Someday, we might like to have a concept of a behaviour assessment, which would specify beliefs off the equilibrium path (for example so we can represent perfect-Bayesian equilibria or sequential equilibria).