Last modified: Tue 1/7/97 2200 PST
As with all Waldzell games, players must agree on the ontology that will underlie their game. For more information, see the description of this step for zeroth-order games.
The starting point of play in a second-order game is a completed first-order game, the template, which is used as described below. This template may be obtained by selecting a completed game from the Game Archive or by playing a first-order game in anticipation of second-order play. In either case, the primary criterion is that the template must be compatible with the ontology to which the players have committed for their second-order game. In fact, it needn't have been played as a first-order game at all: it can also be the analogue (see below) from a second-order game, or even a completed third-order game: all of these forms are indistinguishable by inspection (although they are likely to vary greatly in size and complexity).
Players agree on the order in which they will move, and play in that order throughout the game.
With the selected template game as a "road-map", players complete what is in effect a new first-order game (the analogue). There are two types of move, chosen at the discretion of each player. In the first type, the player introduces a term into the analogue which is intended to mirror a specific term in the template. Relations which mirror those in the template are added to the analogue as soon as both terms mentioned in the assertion have been introduced by players. Obviously, the introduction of an analogous term has the effect of asserting that the referent of that term participates in the semantic structure of the analogue in (at least) the same way as the mirrored template term does in the semantic structure of the template.
In the second type of move, the player makes a single assertion, as in zeroth-order and first-order games, which is not mirrored in the template. The player may add one of the terms mentioned in the new assertion; due to the usual connectivity constraint, she may not add both.
Because second-order games will eventually serve as the skeletons of third-order games, and because no term may be present more than once in a single game network, players may not introduce terms into the second-order analogue which already exist in the template (or in the analogue itself, trivially).
The second-order game is complete (for the purpose of submission to the Game Archive) when all the template terms have been been mirrored by at least one term in the analogue. Actual game play ends when the players choose to stop, but only at the end of a round (each player contributes the same number of moves to the game).