Human-robot interaction and game theory have developed distinct theories of trust for over three decades in relative isolation from one another. Human-robot interaction has focused on the underlying dimensions, layers, correlates, and antecedents of trust models, while game theory has concentrated on the psychology and strategies behind singular trust decisions. Both fields have grappled to understand over-trust and trust calibration, as well as how to measure trust expectations, risk, and vulnerability. This paper presents initial steps in closing the gap between these fields. Using insights and experimental findings from interdependence theory and social psychology, this work starts by analyzing a large game theory competition data set to demonstrate that the strongest predictors for a wide variety of human-human trust interactions are the interdependence-derived variables for commitment and trust that we have developed. It then presents a second study with human subject results for more realistic trust scenarios, involving both human-human and human-machine trust. In both the competition data and our experimental data, we demonstrate that the interdependence metrics better capture social `overtrust' than either rational or normative psychological reasoning, as proposed by game theory. This work further explores how interdependence theory--with its focus on commitment, coercion, and cooperation--addresses many of the proposed underlying constructs and antecedents within human-robot trust, shedding new light on key similarities and differences that arise when robots replace humans in trust interactions.