Bidders in combinatorial auctions face significant challenges when describing their preferences to an auctioneer. Classical work on preference elicitation focuses on query-based techniques inspired from proper learning--often via proxies that interface between bidders and an auction mechanism--to incrementally learn bidder preferences as needed to compute efficient allocations. Although such elicitation mechanisms enjoy theoretical query efficiency, the amount of communication required may still be too cognitively taxing in practice. We propose a family of efficient LLM-based proxy designs for eliciting preferences from bidders using natural language. Our proposed mechanism combines LLM pipelines and DNF-proper-learning techniques to quickly approximate preferences when communication is limited. To validate our approach, we create a testing sandbox for elicitation mechanisms that communicate in natural language. In our experiments, our most promising LLM proxy design reaches approximately efficient outcomes with five times fewer queries than classical proper learning based elicitation mechanisms.

We propose a decentralized market model in which agents can negotiate bilateral contracts. This builds on a similar, but centralized, model of trading networks introduced by Hatfield et al. (2013). Prior work has established that fully-substitutable preferences guarantee the existence of competitive equilibria which can be centrally computed. Our motivation comes from the fact that prices in markets such as over-the-counter markets and used car markets arise from \textit{decentralized} negotiation among agents, which has left open an important question as to whether equilibrium prices can emerge from agent-to-agent bilateral negotiations. We design a best response dynamic intended to capture such negotiations between market participants. We assume fully substitutable preferences for market participants. In this setting, we provide proofs of convergence for sparse markets ({covering many real world markets of interest}), and experimental results for more general cases, demonstrating that prices indeed reach equilibrium, quickly, via bilateral negotiations. Our best response dynamic, and its convergence behavior, forms an important first step in understanding how decentralized markets reach, and retain, equilibrium.