To trust someone implies taking some risk. To be trustworthy implies that you will try to reduce risks to those who trust you even if it is costly to you to do so. For economists trust reduces the transaction cost of trading. In,
Berg, Joyce, John Dickhaut, and Kevin McCabe, "Trust, Reciprocity, and Social History," Games and Economic Behavior, (10)1995, pp. 122-142,
We designed an experiment to study individuals' propensity to be trusting and to be trustworthy in a task we call the investment game. In this game two subjects are each given $10 as a show up fee. One of the subjects is told that he or she will be decision maker one (DM1), and can send any amount (all, none, or some) of the $10 to the other subject (decision maker two, DM2). The rules are simple. Every dollar sent will be tripled by the experimenter before it reaches DM2, who then gets to decide how much of the tripled money to keep and how much to send back to DM1. After DM2’s decision the game is over and subjects leave. We designed the experiment so it was double-blind meaning that neither the subjects, nor the experimenter, new who was matched together, or what subject made what decision. Game theory predicts that as long as DM2 prefers more money to less, DM2 should keep all the money that is sent. Of course, DM1 should then send nothing. But this is now what happened. On average DM1’s send over $5 and roughly one third of the DM2’s reciprocated by sending back more than was originally sent even though the double-blind condition implied no one would know what DM2 really did.