Yurong Chen  陈昱蓉

Stackelberg equilibrium describes the optimal strategies of a player, when she (the leader) first credibly commits to a strategy. Her opponent (the follower) will best respond to her commitment. To compute the optimal commitment, a leader must learn enough follower’s payoff information. The follower can then potentially provide fake information, to induce a different final game outcome that benefits him more than when he truthfully behaves. We study such follower’s manipulation in extensive-form games. For all four settings considered, we characterize all the inducible game outcomes. We show the polynomial-time tractability of finding the optimal payoff function to misreport. We compare the follower’s optimal attainable utilities among different settings, with the true game fixed. In particular, one comparison shows that the follower gets no less when the leader’s strategy space expands from pure strategies to behavioral strategies. Our work completely resolves this follower’s optimal manipulation problem on extensive-form game trees.

Stackelberg equilibria, as functions of the players’ payoffs, can inversely reveal information about the players’ incentives. In this paper, we study to what extent one can learn about the leader’s incentives by actively querying the leader’s optimal commitments against strategically designed followers. We show that, by using polynomially many queries and operations, one can learn a payoff function that is strategically equivalent to the leader’s, in the sense that: 1) it preserves the leader’s preference over almost all strategy profiles; and 2) it preserves the set of all possible (strong) Stackelberg equilibria the leader may engage in, considering all possible follower types. As an application, we show that the information acquired by our algorithm is sufficient for a follower to induce the best possible Stackelberg equilibrium by imitating a different follower type. To the best of our knowledge, we are the first to demonstrate that this is possible without knowing the leader’s payoffs beforehand.A full version of this paper can be found at https://arxiv.org/abs/2302.11829.

This paper considers the hidden-action model of the principal-agent problem, in which a principal incentivizes an agent to work on a project using a contract. We investigate whether contracts with bounded payments are learnable and approximately optimal. Our main results are two learning algorithms that can find a nearly optimal bounded contract using a polynomial number of queries, under two standard assumptions in the literature: a costlier action for the agent leads to a better outcome distribution for the principal, and the agent’s cost/effort has diminishing returns. Our polynomial query complexity upper bound shows that standard assumptions are sufficient for achieving an exponential improvement upon the known lower bound for general instances. Unlike the existing algorithms which relied on discretizing the contract space, our algorithms directly learn the underlying outcome distributions. As for the approximate optimality of bounded contracts, we find that they could be far from optimal in terms of multiplicative or additive approximation, but satisfy a notion of mixed approximation.

In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal social welfare and discuss bidders’ incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints.

Standard methods for aligning large language models with human preferences learn from pairwise comparisons among sampled candidate responses and regularize toward a reference policy. Despite their effectiveness, the effects of sampling and reference choices are poorly understood theoretically. We investigate these effects through Identity Preference Optimization, a widely used preference alignment framework, and show that proper instance-dependent sampling can yield stronger ranking guarantees, while skewed on-policy sampling can induce excessive concentration under structured preferences. We then analyze iterative alignment dynamics in which the learned policy feeds back into future sampling and reference policies, reflecting a common practice of model-generated preference data. We prove that these dynamics can exhibit persistent oscillations or entropy collapse for certain parameter choices, and characterize regimes that guarantee stability. Our theoretical insights extend to Direct Preference Optimization, indicating the phenomena we captured are common to a broader class of preference-alignment methods. Experiments on real-world preference data validate our findings.