But if you really are a selfish player, and you have somehow persuaded the other player to trust you and play "deny" then you should definitely play "confess" to maximize your payoff. With selfish players there is no way to move to ("deny","deny") in a one-shot Prisoners' Dilemma. Cultural change cannot help unless it amounts to a change in payoffs.

[The story would have been different in a coordination game with multiple Pareto-ranked equilibria where a change in beliefs can move you from a bad equilibrium to a good equilibrium.]

In the case of a perfectly selfless person playing with a selfish person yes, that is a place where game theory ceases to be useful. But real altruists are imperfect, and have somewhat different notions of utility and planning horizons. Some games cease to be interesting but others turn from pure conflict to interesting games.

In fact, most of the examples I remember from The Strategy of Conflict are among groups that generally mutually altruistic, like parent and child or soldiers fighting on the same side in a war.

Of course, games played among roughly altruistic players tend to have much better outcomes...