Decentralized Online Learning in General-Sum Stackelberg Games: Strategies for Manipulative and Myopic Followers

Core Concepts

In general-sum Stackelberg games, a strategic follower can manipulate the leader's learning and induce a more favorable equilibrium, while a myopic follower should best respond to the leader's actions.

Abstract

The paper studies decentralized online learning in general-sum Stackelberg games, where players act in a strategic and decentralized manner. It considers two settings based on the information available to the follower:

Limited information setting: The follower only observes its own reward and cannot manipulate the leader. The paper shows that the follower's best strategy is to myopically best respond to the leader's actions, and derives last-iterate convergence results when both players use no-regret learning algorithms.

Side information setting: The follower has extra information about the leader's reward structure. The paper designs a manipulation strategy called FBM for the omniscient follower, and shows that it can gain an intrinsic advantage over the best response strategy. It then extends this to the case of noisy side information, where the follower learns the leader's reward from bandit feedback, and proposes FMUCB, a variant of FBM. The paper derives the sample complexity and last-iterate convergence results for FMUCB.

The key insights are: (1) In the limited information setting, no-regret learning algorithms lead to convergence of Stackelberg equilibrium. (2) In the side information setting, the follower's manipulation strategy can induce a more favorable equilibrium compared to the Stackelberg equilibrium.

Stats

The paper does not contain any explicit numerical data or statistics. It focuses on theoretical analysis and algorithm design.

Quotes

"In the limited information setting, the follower does not know the entire game's payoff matrix, and therefore does not have the ability to manipulate the game. Hence, myopically learning the best response for each action a ∈A is indeed the best strategy for the follower."
"Building on the intuition from the above example, we design FBM, a manipulation strategy for the follower and prove that it gains an intrinsic advantage compared to the best response strategy."
"Another key intuition of FMUCB is to design appropriate UCB terms in place of the true reward terms µl(a, b) and µf(a, b) in FBM, that balances the trade-off between exploration and manipulation."

Key Insights Distilled From

Decentralized Online Learning in General-Sum Stackelberg Games

by Yaolong Yu,H... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.03158.pdf

Deeper Inquiries

How can the proposed algorithms be extended to settings with more complex reward structures, such as non-linear or adversarial rewards

The proposed algorithms can be extended to settings with more complex reward structures by incorporating techniques to handle non-linear or adversarial rewards. For non-linear reward structures, the algorithms can be adapted to handle functions that are not strictly additive or linear. This may involve using function approximation methods or neural networks to estimate the rewards and update the strategies accordingly. Additionally, techniques from reinforcement learning, such as deep Q-learning or policy gradient methods, can be employed to handle non-linear reward functions effectively.
In the case of adversarial rewards, where the rewards of one player directly conflict with the rewards of the other player, the algorithms can be modified to account for the adversarial nature of the game. This may involve incorporating adversarial training techniques to anticipate and counteract the manipulative strategies of the opponent. Adversarial reinforcement learning frameworks can also be utilized to model the interactions between the players in a more adversarial setting.
By extending the algorithms to handle more complex reward structures, such as non-linear or adversarial rewards, the models can better capture the dynamics of real-world scenarios where the reward functions are not simple or cooperative.

What are the implications of the follower's manipulation strategy on the overall social welfare or system efficiency in real-world applications

The follower's manipulation strategy can have significant implications on the overall social welfare or system efficiency in real-world applications, especially in scenarios where strategic interactions between multiple agents impact the outcomes. In settings like security games, auction mechanisms, or resource allocation problems, the follower's ability to manipulate the leader's decisions can lead to suboptimal outcomes or inefficiencies in the system.
If the follower successfully manipulates the leader to deviate from the optimal strategy, it can result in a misallocation of resources, decreased system efficiency, or even security vulnerabilities. This can have detrimental effects on the overall social welfare by reducing the benefits that could be achieved if both players cooperated optimally.
Understanding and mitigating the follower's manipulation strategies are crucial in designing robust and efficient systems. By developing algorithms that can detect and counteract manipulative behaviors, the overall system efficiency can be improved, leading to better outcomes for all stakeholders involved.

Can the insights from this work be applied to other types of sequential decision-making problems beyond Stackelberg games

The insights from this work can be applied to other types of sequential decision-making problems beyond Stackelberg games, especially in scenarios involving strategic interactions between multiple agents. Some potential applications include:

Multi-Agent Reinforcement Learning: The concepts of decentralized learning, strategic manipulation, and no-regret algorithms can be applied to multi-agent reinforcement learning settings. Agents can learn to interact strategically in complex environments, adapting their strategies based on the actions of other agents.

Auction Mechanisms: In auction settings where bidders compete for resources, the principles of strategic manipulation and learning from noisy feedback can be utilized to design more efficient and robust auction mechanisms. Agents can learn to bid strategically to maximize their utility while considering the actions of other bidders.

Resource Allocation: In scenarios where multiple entities compete for limited resources, the ideas of learning in strategic environments can help optimize resource allocation processes. Agents can adapt their strategies based on the actions of others to achieve better outcomes for the overall system.

By applying the insights from decentralized online learning in Stackelberg games to these diverse sequential decision-making problems, we can enhance the efficiency, fairness, and effectiveness of multi-agent systems in various real-world applications.