Large Language Model (LLM)-based multi-agent systems are increasingly used to simulate human interactions and solve collaborative tasks. A common practice is to assign agents with personas to encourage behavioral diversity. However, this raises a critical yet underexplored question: do personas introduce biases into multi-agent interactions? This paper presents a systematic investigation into persona-induced biases in multi-agent interactions, with a focus on social traits like trustworthiness (how an agent's opinion is received by others) and insistence (how strongly an agent advocates for its opinion). Through a series of controlled experiments in collaborative problem-solving and persuasion tasks, we reveal that (1) LLM-based agents exhibit biases in both trustworthiness and insistence, with personas from historically advantaged groups (e.g., men and White individuals) perceived as less trustworthy and demonstrating less insistence; and (2) agents exhibit significant in-group favoritism, showing a higher tendency to conform to others who share the same persona. These biases persist across various LLMs, group sizes, and numbers of interaction rounds, highlighting an urgent need for awareness and mitigation to ensure the fairness and reliability of multi-agent systems.