Sponsored Questions and How to Auction Them

Kshipra Bhawalkar·Alexandros Psomas·Di Wang

View original source ↗Read source document ↗Export metadata ↓

Abstract

Online platforms connect users with relevant products and services using ads. A key challenge is that a user's search query often leaves their true intent ambiguous. Typically, platforms passively predict relevance based on available signals and in some cases offer query refinements. The shift from traditional search to conversational AI provides a new approach. When a user's query is ambiguous, a Large Language Model (LLM) can proactively offer several clarifying follow-up prompts. In this paper we consider the following: what if some of these follow-up prompts can be ``sponsored,'' i.e., selected for their advertising potential. How should these ``suggestion slots'' be allocated? And, how does this new mechanism interact with the traditional ad auction that might follow? This paper introduces a formal model for designing and analyzing these interactive platforms. We use this model to investigate a critical engineering choice: whether it is better to build an end-to-end pipeline that jointly optimizes the user interaction and the final ad auction, or to decouple them into separate mechanisms for the suggestion slots and another for the subsequent ad slot. We show that the VCG mechanism can be adopted to jointly optimize the sponsored suggestion and the ads that follow; while this mechanism is more complex, it achieves outcomes that are efficient and truthful. On the other hand, we prove that the simple-to-implement modular approach suffers from strategic inefficiency: its Price of Anarchy is unbounded.

Explore related subjects

cs.GT cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Kshipra Bhawalkar, Alexandros Psomas, Di Wang. 2025-12-03. Sponsored Questions and How to Auction Them. https://arxiv.org/abs/2512.03975

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Learning in Structured Stackelberg Games

We initiate the study of structured Stackelberg games, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as security games and AI safety, we show how this additional structure can help the leader learn a utility-maximizing policy in both the online and distributional settings. In the online setting, we first prove that standard learning-theoretic measures of complexity do not characterize the difficulty of the leader's learning task. Notably, we find that there exists a learning-theoretic measure of complexity, analogous to the Littlestone dimension in online classification, that tightly characterizes the leader's instance-optimal regret. We term this the Stackelberg-Littlestone dimension, and leverage it to provide a provably optimal online learning algorithm. In the distributional setting, we provide analogous results by showing that two new dimensions control the sample complexity upper- and lower-bound.

cs.GT↗

arXiv2026

Equilibrium and Infeasibility: A new solution concept for games

Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $ψ$-penalized solution as a strategy profile maximizing every player's utility over all her penalty minimizing strategies. A variation of Divide-the-Dollar serves as an illustrative example. We further establish the compatibility with the GNE and the solution to the Nash bargaining.

cs.GT↗

arXiv2026

Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots

We consider sequential Plurality elections in which each voter may abstain or vote for a single candidate. Each voter assigns utilities to all candidates; for each voter, this induces a (weak) order over the candidates. Ties are resolved uniformly at random, and voting has a small positive cost, so that a voter prefers to abstain when their vote cannot change the election outcome. We consider a variant of this model where, for each voter, we additionally specify a prefix of her ranking, so that she is only allowed to vote for a candidate from that prefix (or abstain). We prove that for this variant of the model, deciding whether a designated candidate is among the election winners in a subgame-perfect equilibrium of the associated extensive-form game is PSPACE-complete. This partially resolves an open problem from the work of Desmedt and Elkind [2010].

cs.GT↗