[Bug]: Lemke (via lcp_solve) in mixed behaviors seems to only ever find on equilibrium #671
Description
Where did you find this bug?
Other
What operating system are you using?
macOS
What version of Gambit are you using?
16.4.0
What happened?
For an EFG, lcp_solve uses Lemke-Howson (LH) on the strategic form and Lemke on the sequence form. For both, the docs currently claim that they will find all "accessible" equilibria.
For LH, this seems to work fine. E.g. on an nxn coordination game we find all (2^n)-1 equilibria. For Lemke, it is not really clear how to define a scheme that would find all accessible equilibria (for LH, the choice is which pure strategy to drop; for Lemke, one makes the non-discrete choice of a covering vector). In any case, I have seen no example (from many) where our implementation of Lemke actually finds more than one equilibrium.
Surely Lemke can be used to find more than one, and we should return to this in due course -- see issue #370.
For now, we should remove stop_after as a parameter for Lemke (lcp_solve on an EFG with use_strategic as False), and stop after we find one equilibrium, updating the docs accordingly.