Enhancing Decision-Making with Large Language Models through Multi-Agent Fictitious Play

Improving the task performance of Large Language Models (LLMs) is essential, yet scaling these models faces significant challenges such as diminishing returns and high costs. Multi-Agent Systems (MAS) offer a promising solution by distributing tasks among specialized agents to improve the overall task performance. This can reduce training costs at the expense of increased test time due to the discussion and decision-making process. The decision protocol is a critical component of MAS because it specifies how multiple agents collaborate to create a final solution. This thesis introduces the Multi-Agent LLM (MALLM) framework, which implements and evaluates various decision protocols, namely voting, consensus, and judge decision mechanisms, to simulate multi-agent discussions for conversational task solving. Unlike previous work that used a single decision protocol or tested them on limited datasets, this study systematically examines their impact on a diverse set of tasks, ranging from knowledge-based datasets (MMLU, MMLU-Pro, GPQA) and logic-based datasets (StrategyQA, MuSR, Math-lvl-5, SQuAD 2.0). The results indicate that consensus protocols excel in knowledge-intensive domains while voting and judge protocols are more effective for logic-based tasks. Increasing response diversity through independent solution generation improves decision quality, while changes in information access during the decision process have minimal impact.

Multi-agent debate (MAD) was proposed as a promising approach for ensembling the wisdom of multiple large language models (LLMs) to improve reasoning and provide effective supervision to superhuman LLMs. However, increasing empirical evidence suggests that MAD may not outperform or even significantly underperform single-agent approaches (SA), raising doubts about the benefits of MAD. In this work, we investigate this issue by analyzing the incentive structures of popular MAD paradigms: (i) competitive MAD (CopMAD) where agents compete by holding opposing positions; (ii) consensus-seeking MAD (CosMAD) where agents are driven to seek consensus. We show that both paradigms suffer from debate hacking: CopMAD reduces to a cheap-talk game, where agents produce misleading messages to win the game, while CosMAD filters out informative disagreements for premature consensus. Consequently, agents in both CopMAD and CosMAD fail to jointly resolve the ambiguity and seek the truth. To this end, we introduce ColMAD, a collaborative protocol that reframes MAD as a non-zero-sum game to encourage agents to provide informative while truthful messages. Through extensive benchmarking on challenging tasks such as error detection, we show that ColMAD significantly outperforms previous MAD protocols up to 10 percentage points. Under the same budgets, ColMAD effectively brings non-trivial improvements over SA methods, implying that the protocol design is critical to realizing the potential of MAD.

A central goal of large language model (LLM) research is to build agentic systems that can plan, act, and adapt through sustained interaction with dynamic environments. While recent LLM-based agents exhibit impressive contextual reasoning, their long-horizon decision-making remains fragile, often suffering from objective drift, where goals and plans drift over extended interactions. We introduce Multi$^2$, a hierarchical multi-agent decision-making framework that explicitly decomposes agent behavior into complementary roles. A high-level agent (System 1) focuses on context-aware sub-goal generation using supervised fine-tuning (SFT), while a low-level agent (System 2) executes atomic actions through offline-to-online reinforcement learning (RL) in interactive environments. This separation enables stable long-horizon control, mitigates objective drift, and allows efficient adaptation. Across diverse interactive environments, Multi$^2$ consistently outperforms strong agentic baselines, demonstrating improved robustness and coordination in multi-turn interaction. Beyond performance, we introduce and release three hierarchical benchmark datasets, filling a long-standing gap in training and evaluating hierarchical decision-making for LLM-based agents.