We study the rational behaviors of participants in DAG-Based Distributed Ledgers. We analyze generic algorithms that encapsulate the main actions of participants in a DAG-based distributed ledger: voting for a block, and checking its validity. Knowing that those actions have costs, and validating a block gives rewards to users who participated in the validation procedure, we study using game theory how strategic participants behave while trying to maximize their gains. We consider scenarios with different type of participants and investigate if there exist equilibria where the properties of the protocols are guaranteed. The analysis is focused on the study of equilibria with trembling participants (i.e. rational participants that can do unintended actions with a low probability). We found that in presence of trembling participants, there exist equilibria where protocols properties may be violated.