 Notice that the identity of the players is established by this rule: P is the player who states the thesis, whereas O is the one who chooses her repetition rank first. According to a generalized version of this rule, a play may begin with the opponent stating initial concessions before the thesis is stated. This generalized version will be used in  Section 3.2  whereas, for the sake of simplicity,  Section 2  only considers the rule just presented.