[dlaexadi] abstract swordfighting

incomplete information version:

at the beginning of a turn, you see your opponent's attack.  you choose a defense, which is revealed to the opponent.  attack and defense jointly define the probability that the opponent's attack is successful, and the distribution is sampled.  if the attack succeeds, you lose the game.  if the attack fails, it is your turn to choose an attack.  the defense you chose earlier constrains your possibilities of attack.  the attack you choose will constrain your possibilities of defense next turn if the game continues.

imperfect information version:

at the beginning of a turn, the opponent chooses attack part 1 and attack part 2.  you see part 1 of your opponent's attack.  you choose a defense, then part 2 of the opponent's attack is revealed.  your defense is revealed to the opponent.  your defense and opponent's attack part 2 deterministically define whether the opponent's attack succeeds.  if the attack succeeds, you lose the game.  if the attack fails, you choose your attacks part 1 and part 2, and the opponent chooses a defense after seeing your part 1.  your defense earlier constrains your attack part 1, attack part 1 constrains attack part 2, and attack part 2 constrains defense next move if the game continues.

perfect and complete information version:

there is only one possible part 2 attack following any given part 1 attack (so there is no reason to conceal part 2).  the way to win the game is to maneuver the opponent into a position such that there is no defense against an attack.

simplified imperfect information version:

there is only one possible part 1 attack, so it provides no information.  the information available to the defender is the attacker's defense last move.

fancier imperfect information version:

both attack and defense have a "to be revealed" portion and a portion not revealed that also constrains actions next move.  "to be revealed" contains enough information to score the current move, to determine if there is a winner.  we need a mechanism to force a player to obey self-imposed constraints hidden from the other player.  complicated sequences over many moves can be encoded as strategies as done in game theory.  such sequences could involve changing internal state, not affecting the outcome of the current move.

there are a whole bunch of tables that need to be defined: what attacks can follow what defenses and vice versa, and the probabilistic or deterministic outcomes of attack versus defense.  defining these tables offers infinite possibilities of game design.  for example, an action taken one move can constrain actions many moves down the line.

I think all two-player non-cooperative games can be expressed in this framework.