Taxation search in Boolean games

Agents in a Boolean game have a personal goal represented as a propositional logic formula over a set of Boolean variables, where some of these variables are not necessarily held by the agent. The actions available to each agent are assumed to have some cost, and the agent's secondary goal is to minimize its costs. An interesting problem is to find a taxation scheme that imposes additional costs on the agents' actions such that it incentivizes the agents to reach a stable state. The present paper first theoretically outlines the characteristics of Boolean games for which stabilization can be achieved by applying a taxation scheme. Next, a search method for an appropriate taxation scheme is proposed. The proposed method transforms the Boolean game into an Asymmetric Distributed Constraint Optimization Problem (ADCOP). ADCOPs are a natural representation of Boolean games and enable effective search by using existing algorithms. A Boolean game that represents a traffic light coordination game is used throughout the paper as a clarifying example. Finally, an experimental evaluation of the traffic light example confirms the applicability of the proposed search method and outlines some attributes of the game and the search process.