We investigate the development, maintenance, and breakdown of trust-based cooperative behavior in populations that interact in real time. We introduce a new class of real-time experimental institutions to study the dynamics that emerge among decision makers. Previous research on trust and cooperation has mostly focused on simple non-cooperative two-person games in extensive form. Our point of departure is the observation that previous experiments do not exhaust the general sense in which trust and trustworthiness have been used to explain cooperative behavior in the real world. First, the experimental institutions employed to date are all restricted to discrete time. Although discrete time is very convenient for evaluating theories and conducting experiments, social interactions typically evolve in continuous and real time. Second, most previous experiments have focused on one-shot dyadic interactions. In contrast, our focus is on population dynamics between multiple players in repeated interactions. Third, previous experiments have imposed built-in asymmetry on the players, whereas we are interested in interactions between players, symmetric or not, unencumbered by exogenously defined roles. We propose a new game paradigm, called the Real-Time Trust Game (RTTG), which overcomes these limitations. In addition to a game theoretical investigation of variants of this game, we propose several experiments focusing on the major variables that may affect the evolution or breakdown of trust-based cooperation when the game is iterated in time. These variables include group size, method used to elicit responses (i.e., the decision vs. the strategy method), payoff associated with full cooperation by all the players, uncertainty about the player fraction of the payoff, and the matching protocols that govern interactions within the population of players.