Abstract
The problem of pollution control has been mainly studied in the environmental economics literature where the methodology of game theory is applied for the pollution control. To the best of our knowledge this is the first time this problem is studied from the computational point of view. We introduce a new network model for pollution control and present two applications of this model. On a high level, our model comprises a graph whose nodes represent the agents, which can be thought of as the sources of pollution in the network. The edges between agents represent the effect of spread of pollution. The government who is the regulator, is responsible for the maximization of the social welfare and sets bounds on the levels of emitted pollution in both local areas as well as globally in the whole network. We first prove that the above optimization problem is NP-hard even on some special cases of graphs such as trees. We then turn our attention on the classes of trees and planar graphs which model realistic scenarios of the emitted pollution in water and air, respectively. We derive approximation algorithms for these two kinds of networks and provide deterministic truthful and truthful in expectation mechanisms. In some settings of the problem that we study, we achieve the best possible approximation results under standard complexity theoretic assumptions. Our approximation algorithm on planar graphs is obtained by a novel decomposition technique to deal with constraints on vertices. We note that no known planar decomposition techniques can be used here and our technique can be of independent interest. For trees we design a two level dynamic programming approach to obtain an FPTAS. This approach is crucial to deal with the global pollution quota constraint. It uses a special multiple choice, multi-dimensional knapsack problem where coefficients of all constraints except one are bounded by a polynomial of the input size. We furthermore derive truthful in expectation mechanisms on general networks with bounded degree.
Highlights
The advance of technology and commercial freedom have fused and accelerated the development process in an unprecedented scale
Finding an optimal social welfare solution to our problem, which we call Pollution Game (PG), is NP-hard, that is why we study polynomial time approximation algorithms which can lead to incentive compatible mechanisms
We present a truthful in expectation FPTAS for PG on directed trees by a two level dynamic programming approach and a 3-approximation deterministic truthful mechanism
Summary
The advance of technology and commercial freedom have fused and accelerated the development process in an unprecedented scale. The government, as a regulator, is responsible for allocating the licences to the owners in such a way that the amount of emissions does not exceed certain levels both globally and locally, i.e., the regions around the pollution sources This allocation aims at the maximization of owners’ satisfaction, that is, the social welfare is maximized. The government, as the regulator, can decide to either shut down or keep open a pollution source taking into account the diffusion nature of pollution It sets bounds on the global and local levels of pollution, while trying to optimize the social welfare. As a variant of the first application described above, we consider the case in which the government is allowed to sell licences to the pollution sources instead of deciding to shut them down or keep them open This is a widely used approach to control pollution levels by auctioning a fixed number of licences or pollution allowances. As can be seen by this table our approximations are near best possible under appropriate complexity assumptions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
