Re:

» in a two player game what if one player BELIVES there is an =bserver but there is not. the payoff matrix should change.?

If the hypothetical observer is expected to dole out rewards/punishments as result of the player's actions, the player will =dd the expected rewards to the payoff.

Reputation can be translated into expectation of future reward, based =n a cooperation/defection function of other players.

so how does one determine the matrix without knowing the internal =tate of the player.

By guessing. It seems to be a general learning problem to me; we assume =n initial causal model and update approximating a Bayesian model based =n observation.

For instance, if I want to find out if my opponent is going to defect, I =an make a model of my opponent, where I weight the influence of

• their expected current and future interaction reward with me

• their general principled inertia (people tend to behave consistently, =artially because it makes them generally predictable, and partially =ecause they don't want to consider everything from first principles)

• how much they see me as an end-goal (like a parent sees their =hildren, or a teacher their pupils)

• how much reputation gain they expect from actual and imagined 3rd =arty observation

• how much "virtual" reputation gain/loss they get from defecting from =heir own values.

If one wanted to make a PED style model of this, it is probably too =omplex and perhaps it makes sense to simplify it to a single reputation =actor. But I guess that in actual interactions, this is what we =mplicitly consider.