Artificial Intelligence (AI) and Machine Learning (ML) providers have a responsibility to develop valid and reliable systems. Much has been discussed about trusting AI and ML inferences (the process of running live data through a trained AI model to make a prediction or solve a task), but little has been done to define what that means. Those in the space of ML- based products are familiar with topics such as transparency, explainability, safety, bias, and so forth. Yet, there are no frameworks to quantify and measure those. Producing ever more trustworthy machine learning inferences is a path to increase the value of products (i.e., increased trust in the results) and to engage in conversations with users to gather feedback to improve products. In this paper, we begin by examining the dynamic of trust between a provider (Trustor) and users (Trustees). Trustors are required to be trusting and trustworthy, whereas trustees need not be trusting nor trustworthy. The challenge for trustors is to provide results that are good enough to make a trustee increase their level of trust above a minimum threshold for: 1- doing business together; 2- continuation of service. We conclude by defining and proposing a framework, and a set of viable metrics, to be used for computing a trust score and objectively understand how trustworthy a machine learning system can claim to be, plus their behavior over time.

Behavioral experiments on the trust game have shown that trust and trustworthiness are universal among human beings, contradicting the prediction by assuming \emph{Homo economicus} in orthodox Economics. This means some mechanism must be at work that favors their emergence. Most previous explanations however need to resort to some factors based upon imitative learning, a simple version of social learning. Here, we turn to the paradigm of reinforcement learning, where individuals update their strategies by evaluating the long-term return through accumulated experience. Specifically, we investigate the trust game with the Q-learning algorithm, where each participant is associated with two evolving Q-tables that guide one's decision making as trustor and trustee respectively. In the pairwise scenario, we reveal that high levels of trust and trustworthiness emerge when individuals appreciate both their historical experience and returns in the future. Mechanistically, the evolution of the Q-tables shows a crossover that resembles human's psychological changes. We also provide the phase diagram for the game parameters, where the boundary analysis is conducted. These findings are robust when the scenario is extended to a latticed population. Our results thus provide a natural explanation for the emergence of trust and trustworthiness without external factors involved. More importantly, the proposed paradigm shows the potential in deciphering many puzzles in human behaviors.