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.

Two incentive mechanisms for Boolean games were proposed recently - taxation schemes and side payments. Both mechanisms have been shown to be able to secure a pure Nash equilibrium (PNE) for Boolean games. A complete characterization of outcomes that can be transformed to PNEs is given for each of the two incentive mechanisms. Side payments are proved to be a weaker mechanism in the sense that the outcomes that they can transform to PNEs are a subset of those transformable by taxation. A family of social-network-based Boolean games, which demonstrates the differences between the two mechanisms for securing a PNE, is presented. A distributed search algorithm for finding the side payments needed for securing a PNE is proposed. An empirical evaluation demonstrates the properties of the two mechanisms on the family of social-network-based Boolean games.

We investigate the problem of influencing the preferences of players within a Boolean game so that, if all players act rationally, certain desirable outcomes will result. The way in which we influence preferences is by overlaying games with taxation schemes. In a Boolean game, each player has unique control of a set of Boolean variables, and the choices available to the player correspond to the possible assignments that may be made to these variables. Each player also has a goal, represented by a Boolean formula, that they desire to see satisfied. Whether or not a player’s goal is satisfied will depend both on their own choices and on the choices of others, which gives Boolean games their strategic charac- ter. We extend this basic framework by introducing an external principal who is able to levy a taxation scheme on the game, which imposes a cost on every possible action that a player can choose. By designing a taxation scheme appropriately, it is possible to perturb the preferences of the players, so that they are incentivised to choose some equilibrium that would not otherwise be chosen. After motivating and formally presenting our model, we explore some issues surrounding it, including the complexity of finding a taxation scheme that implements some socially desirable outcome, and then discuss desirable properties of taxation schemes.