What if two economists play the prisoner's dilemma?

I was asked an interesting question that 'what if two economists play the prisoner's dilemma together'. To be honest, in principle, it does not matter who is playing the game, the outcome of the prisoner's dilemma does not change, as it is the Nash equilibrium.

However, we can still imagine there are two economists playing the same game. We call them economists because we assume they understand the outcome of the prisoner's dilemma is not the best mutually beneficial outcome and they try to be 'smart' to outperform the others and they know each other well as they work in the field.

With these assumptions, we actually add one more assumption that they have the incentive to cooperate together. However, they do not know each other's possibility of choosing to cooperate, the only thing they know about if the willingness to cooperate is higher than the willingness to 'betary' his/her profession. This leads to a change in their preferences, as the payoff of cooperation increases and the payoff of defection decreases due to their professional 'pride'. Then we need to introduce risk preference into our model and the less risk averse the economists are, the more likely they are to cooperate.

Therefore, in fact, they may have a much greater chance to choose to cooperate. However, the model is no longer a prisoner's dilemma model, as the change in the payoffs of cooperation and defection due their professional 'pride' may change the basic structure of the model and they have a rough knowledge about each other and they can respond to each other's expected strategy.