Bear and Rand (2016) propose a model of the evolution of dual-process decision making, where both intuition and deliberation can play a role. They find that selection can favour dual-process agents who intuitively cooperate, but sometimes use deliberation to defect in one-shot games, while it never favours agents that  intuitively defect, but sometimes use deliberation to override their selfish impulses. We generalize their model in three ways.

1. The cost an individual would have to pay to deliberate is uniformly distributed in Bear and Rand (2016). We allow for general distributions, and find that with hump-shaped distributions — like the normal distribution — selection can also favour dual process defectors who use deliberation to override selfish impulses.
2. We un-collapse the strategy space for the repeated game, and find that “waiting” equilibria exist, where players do not deliberate in order to find out whether the interaction is repeated or one-shot, but wait for time to tell.
3. We allow for players to observe whether or not the other deliberates. This allows players to strategically choose not to deliberate, as in Hoffman et al.  (2015).

(Joint with Matthijs van Veelen)