Tradable credit schemes (TCS) have been receiving increasing attention as an alternative to congestion pricing due to considerations of equity and revenue neutrality. Although it is typically assumed that credit transactions occur between travelers directly, i.e., via peer-to-peer (P2P) trading, the underlying mechanism that achieves market clearing (in terms of matching of sellers and buyers and pricing of credits) has not been studied in sufficient detail. This study extends the current literature on TCS by proposing two types of P2P trading paradigms that define the rules of matching selling and buying orders, market price adjustment, and the individual bidding format. Together with a peer-to-regulator (P2R) design, all trading paradigms are tested in the context of the morning commute problem under a given distance-based time-of-day credit tariff scheme. Numerical results demonstrate that the proposed P2P trading paradigms – in the absence of transaction costs – lead to a near identical equilibrium in terms of social welfare gains, departure flows, and credit price as that obtained from P2R schemes. Further, the P2P trading mechanisms ensure budget neutrality of credits as well as revenue neutrality of the regulator during the day-to-day process.