Designing Incentives for Boolean Games

Boolean games are a natural, compact, and expressive class of logic-based games, in which each player exercises unique control over some set of Boolean variables, and has some logical goal formula that it desires to be achieved. A player's strategy set is the set of all possible valuations that may be made to its variables. A player's goal formula may contain variables controlled by other agents, and in this case, it must reason strategically about how best to assign values to its variables. In the present paper, we consider the possibility of overlaying Boolean games with taxation schemes. A taxation scheme imposes a cost on every possible assignment an agent can make. By designing a taxation scheme appropriately, it is possible to perturb the preferences of the agents within a society, so that agents are rationally incentivised to choose some socially desirable equilibrium that would not otherwise be chosen, or incentivised to rule out some socially undesirable equilibria. After formally presenting the model, we explore some issues surrounding it (e.g., the complexity of finding a taxation scheme that implements some socially desirable outcome), and then discuss possible desirable properties of taxation schemes.