Large Language Models (LLMs) are increasingly applied to software engineering (SE), yet their potential for autonomous, role-oriented collaboration remains largely underexplored. Understanding how multiple LLM-based agents coordinate, maintain role alignment, and converge on solutions is critical for SE, as naively allowing agents to interact does not reliably lead to correct or stable outcomes. Recent empirical studies show that unstructured or poorly understood interaction dynamics can result in error propagation, premature consensus on incorrect solutions, or prolonged disagreement that prevents convergence, even when correct partial solutions are present early in the interaction. As an initial step towards addressing this underexplored area, we undertake a systematic analysis of conversations between two agents, a Designer and a Programmer across 12 model combinations from 7 open-source LLMs (Gemma 2, Gemma 3, LLaMA 3.2, LLaMA 3.3, DeepSeek-R1, MiniCPM, and Qwen3). Our systematic approach reveals three key dimensions of multi-agent interaction: efficiency (the speed and stability of convergence), consistency (the degree of role alignment visualized by BLEU and ROUGE), and effectiveness (the extent of compilation success and error resolution). Results show that the DeepSeek-R1:DeepSeek-R1 pair was unique in converging to the correct solution from the very first iteration and sustaining it consistently to the final iteration, while LLaMA 3.2:LLaMA 3.2 and Qwen3:Qwen3 demonstrated strong Designer:Programmer role alignment despite of diverging from the correct solution. The other pairs deviated from the task, never to converge to a result. These findings advance understanding of agentic programming and highlight the need for further research on understanding and calibrating convergence and stop conditions essential for future autonomous SE.