Press and Dyson’s setup had two areas where ‘strategies’ come into play.
The first area is the set of four probabilities you provide to the game, which determine your score when combined with the other player’s set of four probabilities. Tit-for-tat is one particular choice of four probabilities (and, based on the nature of the game, should actually be represented as “slightly forgiving tit-for-tat”, which cooperates with probability epsilon in the defect-defect or defect-cooperate case, so that when playing against itself all states will terminate with cooperate-cooperate).
The second area is how the players modify those sets over time. Here, ‘theory of mind’ is relevant: both players with and without theories of mind can play any particular 4-probability set, like tit-for-tat. Players with theory of mind think (at least) two steps ahead- when I change my probabilities, how will my opponent change their probabilities? Players without theory of mind think only one step ahead- given my opponent’s probabilities, which play maximizes my score?
Press and Dyson’s setup had two areas where ‘strategies’ come into play.
The first area is the set of four probabilities you provide to the game, which determine your score when combined with the other player’s set of four probabilities. Tit-for-tat is one particular choice of four probabilities (and, based on the nature of the game, should actually be represented as “slightly forgiving tit-for-tat”, which cooperates with probability epsilon in the defect-defect or defect-cooperate case, so that when playing against itself all states will terminate with cooperate-cooperate).
The second area is how the players modify those sets over time. Here, ‘theory of mind’ is relevant: both players with and without theories of mind can play any particular 4-probability set, like tit-for-tat. Players with theory of mind think (at least) two steps ahead- when I change my probabilities, how will my opponent change their probabilities? Players without theory of mind think only one step ahead- given my opponent’s probabilities, which play maximizes my score?