# Imitative Follower Deception in Stackelberg Games

## TL;DR

This paper investigates how a leader in Stackelberg games can mitigate losses caused by followers who strategically imitate other types, proposing models and algorithms to design robust leader strategies against such deception.

## Contribution

The paper introduces a model of follower deception in Stackelberg games and analyzes the computational complexity of deriving optimal leader policies under deception.

## Key findings

- Leader can reduce losses with carefully designed policies.
- Computational complexity varies across different model variants.
- Follower deception significantly increases the difficulty of strategy computation.

## Abstract

Information uncertainty is one of the major challenges facing applications of game theory. In the context of Stackelberg games, various approaches have been proposed to deal with the leader's incomplete knowledge about the follower's payoffs, typically by gathering information from the leader's interaction with the follower. Unfortunately, these approaches rely crucially on the assumption that the follower will not strategically exploit this information asymmetry, i.e., the follower behaves truthfully during the interaction according to their actual payoffs. As we show in this paper, the follower may have strong incentives to deceitfully imitate the behavior of a different follower type and, in doing this, benefit significantly from inducing the leader into choosing a highly suboptimal strategy. This raises a fundamental question: how to design a leader strategy in the presence of a deceitful follower? To answer this question, we put forward a basic model of Stackelberg games with (imitative) follower deception and show that the leader is indeed able to reduce the loss due to follower deception with carefully designed policies. We then provide a systematic study of the problem of computing the optimal leader policy and draw a relatively complete picture of the complexity landscape; essentially matching positive and negative complexity results are provided for natural variants of the model. Our intractability results are in sharp contrast to the situation with no deception, where the leader's optimal strategy can be computed in polynomial time, and thus illustrate the intrinsic difficulty of handling follower deception. Through simulations we also examine the benefit of considering follower deception in randomly generated games.