Scrabble

The game of scrabble obviously has many ways in which a player can gain an unfair advantage by means of a compromise. There is however a rule in this game which incorporates the notion of untrustworthy players.

The basic rules of the game allow you to play any letter combination on the board that you please -- the board, the pieces, and the scoring will do nothing directly to stop you (although it does state which types of words you are allowed to play).

So along comes a player who decides to put words on the board that aren't real. Another player dislikes this "supposed" word. The rules of scrabble include a manner by which this tension between the two players can be resolved: the challenge.

If one player feels strongly enough that the word another player has created is not genuine, he can challenge that player, which becomes a miniature game in itself (and if you draw the game score matrix you will see it has a similar pattern to the prisoner's dilemma).

This challenge rule has essentially eliminated the game compromise* of playing an invalid word. Rather it has made invalid words a viable and manageable aspect to a game strategy.

Scrabble therefore demonstrates one of the methods to mitigate game compromise: include the known manners of cheating in the rules of the game.

This actually allows computer opponents to cheat quite easily, as it would take more work to program an opponent that didn't have perfect recollection of the entire dictionary than one that did. Thereby the cheapest computer opponent will always notice every invalid word and will always wage a successful challenge.

The Prisoner's Dilemma

One of the more popular games that is used to demonstrate ideas in logic or game theory is the "Prisoner's Dilemma".

In this game the best strategy (rational strategy) of the players is such that they will not realize the most beneficial outcome. However, if the game activity were compromised, we can quickly see a strategy that develops which achieves better results (for at least a few players).

If the prisoners can, unbeknownst to the guards, communicate (a compromise of the game), they will always get better results -- but to the guards they will be acting irrationally because from the guards view the prisoners are not following the best strategy.

The presence of a compromise alters the dynamics of any game that could benefit from coordination. In particular a compromise tends to upset the Nash equilibrium (allowing a single person to change their strategy and have a gain, without having any other person change their strategy -- even though the rules dictate this cannot be possible).

Example

In the prisoner's dilemma we introduce a cheat by stating that prisoner A knows what prisoner B's choice is before making his own. This then reduces the possible score B has in the game (but B will be unaware of this reduced possibility). In this case, A's strategy is:
1) if B defects then defect, minimize A's loss
2) if B cooperates, then what A does is determined by his intentions towards B (he can cooperate with no fear of being deceived)

Should B become aware of A's ability to cheat then B has only two options:
1) choose to cooperate and be left to A's whims as to the outcome
2) choose to defect and ensure that A also defects

If we introduce one more cheat that allows B to understand A's intentions, then B can simply make his choice by examining his own best outcome in the strategy of A:
1) if A intends to deceive B, then B will choose to defect
2) if A intends not to deceive B, then B will choose to cooperate

Do note now that with these two cheats, and the final strategy of B, and the strategy of A, we appear to have a Nash equilibrium again.