Algorithm 6 LLM-Mediated Agent Negotiation Protocol
1:Input: Agents $A_1$, $A_2$; initial offers ${\mathcal{O}}_1$, ${\mathcal{O}}_2$; LLM model $\mathcal{L}$; negotiation limit T   2:Output: Final agreement $\mathcal{A}$ or failure   3:Initialize history buffer $\mathcal{H}\leftarrow \varnothing$   4:for$t=1$ to T do   5:    $A_1$ generates offer ${\mathcal{O}}_1^t$ based on local state and preferences   6:    $A_2$ generates counter-offer ${\mathcal{O}}_2^t$ based on prior offer and utility evaluation   7:    Append $({\mathcal{O}}_1^t,{\mathcal{O}}_2^t)$ to $\mathcal{H}$
8:    ${\mathcal{S}}_t\leftarrow \mathcal{L}\left(\mathcal{H}\right)$	▹ LLM summarizes intents and preferences
9:    Compute utility scores $U_1,U_2$ from ${\mathcal{S}}_t$ 10:      if $U_1\ge {\tau }_1$ and $U_2\ge {\tau }_2$ then 11:          return Agreement $\mathcal{A}\leftarrow ({\mathcal{O}}_1^t,{\mathcal{O}}_2^t,{\mathcal{S}}_t)$ 12:      else 13:          Agents update proposal strategy based on feedback or regret 14:      end if 15:end for 16:return Negotiation failed