Given a fixed state of knowledge about possible opponents and finite number of feasible options for your decision, there will be maximal decisions, even if in an iterated contest the players could cycle their decisions against updated opponents indefinitely.
Hmm if it was a programming contest I would expect non-transitive ‘betterness’.
Given a fixed state of knowledge about possible opponents and finite number of feasible options for your decision, there will be maximal decisions, even if in an iterated contest the players could cycle their decisions against updated opponents indefinitely.