Decentralized leadership and follower deception in Stackelberg games
Keywords: mechanism design
strategy commitment
imitative deception
defense coordination
Nash-Stackelberg equilibrium
Stackelberg games
security games
learn to commit

This thesis focuses on two aspects of Stackelberg games — decentralized leadership and follower deception — that stem from reasoning about strategic interactions at a higher level in Stackelberg games.
In the first part of the thesis, we study decentralized leadership in Stackelberg games. We focus on a variant of Stackelberg security games that involves multiple leaders, in which the leaders allocate their security resources to protect a set of targets against an attacker; the attacker acts as the follower in the game, surveying the leaders’ strategies and responding rationally afterwards. We aim to understand the game under decentralized leadership and explore ways to coordinate the leaders. To this end, firstly, we propose a novel equilibrium concept to describe the outcome of the game, and we analyze the existence of an equilibrium and the complexity of computing it. Then, we take a mechanism design approach to coordinate the leaders, aiming to design a coordination mechanism that satisfies several natural properties concerning efficiency, incentives, strategyproofness, and stability of strategies it generates. We obtain impossibility results showing that certain combinations of these properties cannot be achieved by any mechanism. On top of that we also present mechanisms for property combinations that are not blocked by the impossibility results.
The second part of the thesis is motivated by the finding that, in a Stackelberg game, the follower can benefit from changing the leader’s belief about the game. This can typically happen when the follower is able to tamper with the leader’s attempt of information gathering: for instance, when the leader learns the follower’s type by interacting with the follower, the follower can imitate the behavior of a different follower type, pretending that their payoffs are different than the actual ones. A leader who ignores such strategic manipulation will then be misled into playing optimally against the imitated follower type, which may correspond to a highly suboptimal strategy in the original game. We study the strategic interactions resulting from this deceptive behavior, both from the leader’s and the follower’s perspectives. From the leader’s perspective, we propose a policy-based approach to mitigate potential losses due to follower deception and study the associated problem of computing the optimal policy. From the follower’s perspective, we study the problem of computing the optimal strategy to deceive the leader. Our results provide an almost complete picture of the complexity landscape of these problems in various settings. It is shown that the problems facing the leader are hard in general, whereby we derive inapproximability bounds and also design algorithms that achieve matching approximation ratios; whereas the problems facing the follower are tractable, whereby we design polynomial-time algorithms to compute optimal (or near-optimal) deception strategies for the follower.
Our work sheds light on strategic interactions that may arise in Stackelberg games but are not captured by existing solution concepts. It provides frameworks to study these interactions and contributes to the understanding of them through the lens of computation.