The Inference Report

Understanding the objectives that drive agents' behavior is crucial in strategic environments, where multiple agents interact and adapt to one another. This challenge arises in domains such as cybersecurity, autonomous driving, and online markets, where agents' underlying incentives are typically unknown and must be inferred from their observed behavior. Inverse reinforcement learning (IRL) provides a natural framework for this problem, but extending IRL to strategic multi-agent settings introduces a fundamental challenge: a reward that explains observed behavior does not necessarily induce optimal strategies when used for decision-making. In this work, we study this problem through the lens of \emph{strategic identifiability}, and show that learning from a fixed policy pair can be insufficient to strategically identify rewards, independent of the number of expert samples $K$. Motivated by this, we introduce an active IRL algorithm for two-player repeated Stackelberg games, in which the leader adaptively selects policies to elicit informative responses about the follower's reward. Combining maximum-likelihood estimation with experimental design, we derive finite-sample guarantees on the Stackelberg sub-optimality induced by the learned reward, matching up to polylogarithmic factors a new minimax learning rate of $K^{-1/2}$. Finally, we evaluate our approach in a realistic anti-poaching setting, demonstrating the benefits of active exploration for reward recovery and downstream strategic performance.

We present a scalable framework for solving multi-step tasks through a decentralized market of self-interested agents. Prior theoretical work demonstrated that agents organized through sequential auctions can converge to a globally optimal policy in a Markov decision process (MDP), but relied on the restrictive assumption of the existence of perfect clones as a model of perfect competition. In reality, exact clones drive agent profit to zero, violating the natural risk-reward incentives of participants. Conversely, we empirically demonstrate that the opposite extreme, absence of competition, also leads to market failure and value extraction collapse. Between these two extremes, we investigate how heterogeneous agents can survive in markets that span the critical middle ground of imperfect competition. To be profitable, agents learn to strategically shade bids to secure positive individual profit margins, while still ensuring that the marketplace functions effectively enough so that collaborative tasks posed by market consumers can still be solved. We formulate and evaluate four bidding algorithms (Mirror Descent, Thompson Sampling, Bayes-Optimal, and PPO) across three auction protocols (1st-Price, 2nd-Price, and Credit-Conserving Vickrey). Across a diverse set of domains, we demonstrate that imperfect competition successfully sustains necessary agent profit margins while maintaining high task success rates at low costs.

We study packet routing in queuing systems where queues act as selfish, myopic agents that use no-regret learning algorithms to select servers with unknown service rates. To model the small buffers used in data centers, we assume that each server has a single-packet buffer. Even such a tiny buffer already captures the features of buffering: routers can exploit multiple servers while accepted packets remain in service, but packets can occupy servers for multiple rounds, complicating future service and learning. We first analyze a single queue routing packets to $m$ buffered servers with service rates $μ_1, \dots, μ_m$. This setting is equivalent to an instance of the recharging bandits problem with geometric recharge. We prove that any no-regret learner achieves a long-run average throughput of at least the Hamacher sum of the server rates, and that this bound is tight. Consequently, a single no-regret queue is stable if and only if its arrival rate is below the Hamacher sum of the server rates. Moreover, comparing against an optimal policy, we show that any no-regret learner is at least $0.77$-competitive, which is also tight. We then study multi-queue systems where $n$ queues with arrival rates $λ_1, \dots, λ_n$, each at most $λ_{\max}$, compete for service from $m$ buffered servers. We show that the smallest overprovisioning factor that guarantees the system to be stable under high-probability no-regret learning is $\frac{1}{1-λ_{\max}}$. Equivalently, in terms of the total arrival and service rates, the condition $\sum_{i=1}^n λ_i < (1-λ_{\max})\sum_{j=1}^m μ_j$ is sufficient, and sometimes necessary, for stability under no-regret learning. In particular, for $λ_{\max} = 1/2$, this improves the upper bound of Abel et al. (EC 2026) from $3$ to $2$, matching their lower bound and resolving their open question.

Assigning routine tasks to cheaper large language model (LLM) providers can reduce generation cost, but switching providers may require processing accumulated context again. Keeping dependent tasks with the same provider can instead reuse eligible context. Graph-based workflows therefore couple routing decisions across tasks. Independent providers may also privately know their real-time unit costs and strategically misreport them. We formulate this routing problem as a single-parameter procurement auction and propose STAR (Strategy-proof Topology-aware Agent Routing), which minimizes virtual-cost-weighted graph workloads. Its allocation rule and payments, computed by integrating workload over possible cost reports, make truthful reporting utility-maximizing regardless of other providers' reports and cover each truthful provider's execution cost. With independent cost distributions and non-decreasing virtual costs, STAR additionally minimizes the user's expected total payment to providers. Controlled synthetic experiments separate the execution-cost benefit of topology awareness from the payment benefit of virtual-cost optimization: the former grows with fan-out and transferred payload, while the latter increases gradually along the tested prior-shape heterogeneity path. A paired sensitivity study quantifies how payment savings vary with prior misspecification while strategy-proofness is preserved.

We prove that computing a complete contiguous $\varepsilon$-envy-free cake allocation is PPAD-complete for normalized rational piecewise-constant additive valuations. The hardness holds even when $\varepsilon$ is given in unary, and even when every density takes only two values, which are the same for all agents, and is piecewise constant with at most six breakpoints. As a consequence, computing an exact contiguous envy-free allocation is also PPAD-complete, and the hardness holds under the same restrictions on the densities. Our key ingredient is to assign prices to the pieces so that, in every approximately envy-free allocation, all prices are nearly equal, regardless of how the pieces are assigned to the agents. We further show that, for every fixed integer $c\ge1$, computing a contiguous EF$c$ allocation of indivisible goods on a path is PPAD-complete for additive valuations, and the hardness holds even for binary valuations in which each good is valued by exactly one agent and all agents value the same number of goods.

Pairwise comparison data are a standard supervision signal in preference learning, but disagreement in such data can reflect stable latent heterogeneity, ephemeral stochasticity, or non-binary responses hidden by a forced-choice interface. We study which of these semantic distinctions are identifiable from the feedback channel itself. We introduce a nonparametric latent semantic model with three querywise quantities: aggregate directional preference $μ_q$, persistent disagreement $τ_q$, and non-binary mass $α_q$. Under the anonymous binary channel, we prove an exact semantic fiber theorem: $μ_q$ is point-identified, whereas $(τ_q, α_q)$ vary over an explicit feasible region compatible with the same binary law. Same-annotator repeats identify $τ_q$ through a covariance identity, abstention-enabled feedback identifies $α_q$ directly, and together they point-identify the full semantic triple. We also derive finite-sample estimators, nonasymptotic concentration bounds, and semantics-aware action-recovery guarantees, and validate the theory on theorem-matched synthetic data.