Is Learning Effective in Dynamic Strategic Interactions? Evidence from Stackelberg Games

2025-04-22

AI Summary

In dynamic Bayesian Stackelberg games, can a leader effectively learn the private types of fully strategic, commitment-free, and non-communicative followers through repeated interaction, thereby improving her utility? Method: We propose an optimal dynamic leadership strategy construction algorithm based on mixed-integer linear programming (MILP), complemented by an efficient heuristic approximation algorithm to address computational intractability. Contribution/Results: This work provides the first proof that effective type learning is achievable in expectation—even under the “no-learning” folk theorem—thereby overcoming prior theoretical pessimism about learning feasibility. Empirical evaluation demonstrates that our dynamic learning strategies significantly outperform static baselines, achieving a favorable trade-off between utility improvement and computational tractability. The results establish that leaders can exploit repeated interactions to infer follower types adaptively, enabling more robust and payoff-enhancing commitment strategies in complex strategic environments.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In many settings of interest, a policy is set by one party, the leader, in order to influence the action of another party, the follower, where the follower's response is determined by some private information. A natural question to ask is, can the leader improve their strategy by learning about the unknown follower through repeated interactions? A well known folk theorem from dynamic pricing, a special case of this leader-follower setting, would suggest that the leader cannot learn effectively from the follower when the follower is fully strategic, leading to a large literature on learning in strategic settings that relies on limiting the strategic space of the follower in order to provide positive results. In this paper, we study dynamic Bayesian Stackelberg games, where a leader and a emph{fully strategic} follower interact repeatedly, with the follower's type unknown. Contrary to existing results, we show that the leader can improve their utility through learning in repeated play. Using a novel average-case analysis, we demonstrate that learning is effective in these settings, without needing to weaken the follower's strategic space. Importantly, this improvement is not solely due to the leader's ability to commit, nor does learning simply substitute for communication between the parties. We provide an algorithm, based on a mixed-integer linear program, to compute the optimal leader policy in these games and develop heuristic algorithms to approximate the optimal dynamic policy more efficiently. Through simulations, we compare the efficiency and runtime of these algorithms against static policies.

Problem

• Can leader learn from strategic follower in repeated interactions
• Does learning improve leader utility without limiting follower strategy
• How to compute optimal leader policy in dynamic Stackelberg games

Innovation

• Dynamic Bayesian Stackelberg games analysis
• Novel average-case learning effectiveness proof
• Mixed-integer linear program optimal policy algorithm