We consider the problem of incentivising desirable behaviours in multi-agent systems by way of taxation schemes. Our study employs the concurrent games model: in this model, each agent is primarily motivated to seek the satisfaction of a goal, expressed as a Linear Temporal Logic (LTL) formula; secondarily, agents seek to minimise costs, where costs are imposed based on the actions taken by agents in different states of the game. In this setting, we consider an external principal who can influence agents' preferences by imposing taxes (additional costs) on the actions chosen by agents in different states. The principal imposes taxation schemes to motivate agents to choose a course of action that will lead to the satisfaction of their goal, also expressed as an LTL formula. However, taxation schemes are limited in their ability to influence agents' preferences: an agent will always prefer to satisfy its goal rather than otherwise, no matter what the costs. The fundamental question that we study is whether the principal can impose a taxation scheme such that, in the resulting game, the principal's goal is satisfied in at least one or all runs of the game that could arise by agents choosing to follow game-theoretic equilibrium strategies. We consider two different types of taxation schemes: in a static scheme, the same tax is imposed on a state-action profile pair in all circumstances, while in a dynamic scheme, the principal can choose to vary taxes depending on the circumstances. We investigate the main game-theoretic properties of this model as well as the computational complexity of the relevant decision problems.

翻译：我们研究通过税收方案激励多智能体系统中理想行为的问题。我们的研究采用并发博弈模型：在该模型中，每个智能体主要动力源自追求满足个人目标，该目标以线性时态逻辑公式表示；其次，智能体力求最小化成本，其中成本根据博弈不同状态下智能体采取的行动而施加。在此设定下，我们考虑一个外部委托方，其能通过在不同状态下对智能体选择的行动施加税收（额外成本）来影响智能体的偏好。委托方实施税收方案以激励智能体选择行动路径，从而达成同样以线性时态逻辑公式表达的委托方目标。然而，税收方案对智能体偏好的影响力有限：无论成本如何，智能体始终优先满足自身目标而非其他目标。我们研究的核心问题是：委托方是否能设计税收方案，使得在由此产生的博弈中，当智能体遵循博弈论均衡策略时，委托方目标能在至少一次或全部可能的博弈运行中得到满足。我们考虑两类税收方案：静态方案中，同一状态-行动组合在所有情形下被施加固定税率；动态方案中，委托方可依据情形调整税率。本文探究该模型的主要博弈论性质及相关决策问题的计算复杂性。