Dialogue agents that support human users in solving complex tasks have received much attention recently. Many such tasks are NP-hard optimization problems that require careful collaborative exploration of the solution space. We introduce a novel dialogue game in which the agents collaboratively solve a two-player Traveling Salesman problem, along with an agent that combines LLM prompting with symbolic mechanisms for memory, state tracking and problem-solving. Our best agent solves 45% of games optimally in self-play. It also demonstrates an ability to collaborate successfully with human users and generalize to unfamiliar graphs.

Collaboration is an integral part of human dialogue. Typical task-oriented dialogue games assign asymmetric roles to the participants, which limits their ability to elicit naturalistic role-taking in collaboration and its negotiation. We present a novel and simple online setup that favors balanced collaboration: a two-player 2D object placement game in which the players must negotiate the goal state themselves. We show empirically that human players exhibit a variety of role distributions, and that balanced collaboration improves task performance. We also present an LLM-based baseline agent which demonstrates that automatic playing of our game is an interesting challenge for artificial systems.