Cooperate without looking in a non-repeated game

We propose a simple model for why we have more trust in people who cooperate without calculating the associated costs. Intuitively, by not looking at the payoffs, people indicate that they will not be swayed by high temptations to defect, which makes them more attractive as interaction partners. We capture this intuition using a simple four-stage game. In the first stage, nature draws the costs and benefits of cooperation according to a commonly-known distribution. In the second stage, Player 1 chooses whether or not to look at the realized payoffs. In the third stage, Player 2 decides whether to exit or let Player 1 choose whether or not to cooperate in the fourth stage. Using backward induction, we provide a complete characterization for when we expect Player 1 to cooperate without looking. Moreover, we show with numerical simulations how cooperating without looking can emerge through simple evolutionary processes.