The Analysis Of Emission Firm In An Oligopoly Supergame

Game theory is about the decision and equilibrium of policy-making when their actions directly interact each other. In the equilibrium, each player's utility function not only depends on his own chosen strategy, but also depends on other player's chosen strategy. Therefore, game theory is about research on problem of individual choice under the external economic condition. The Nash equilibrium is inevitablely reached when N people participate in the Game. It's a strategic combination formed by the optimal strategy of all participants. Namely, given a strategy of others, single person has no interest in other strategic options, so that nobody would break the equilibrium. As a typical case, "Prisoners' Dilemma" reflects a profound contradiction of personal rationality and collective rationality. For example, in the issue of economic reform, reformers must pay the cost (including risk), but all the people share the fruits of the reform. As a result, nobody truly wants to reform, though people think that the reform is good, and everybody has to continue to live with the dissatisfied system.After several decades of rapid development, Game theory has made tremendous achievements both in the theoretical studies and applied research. The supergame theory created by Aumann is one of the most important works. Supergame, namely, an infinitely repeated game, its basic idea is that after a certain discount factor is chosen and the players learn from each other and interact in the course of repeated games, the players can reach a binding "tacit agreement" consciously. Thus, the collective rationality can be possibly reached. In order to avoid punishes, players may implement the optimal choice for collective conscientiously, and thereby avoid in a "prisoners' dilemma" situation. This paper is based on a four-stage sequential game in a super game market. It explores the link between an environmental regulatory instrument and the capital structure and output decisions of firms if once the collusion can be reached. The government is the first mover and determines the level of environmental regulation by setting a emission tax. Given knowledge of the policy settings, firms determine their capital structure by choosing debt levels in the second stage. Once debt levels have been determined, firms then decide on the optimum level of pollution abatement. Finally, given information about the policy instruments, capital structure and abatement levels, the output levels are chosen. In the analysis process, this paper makes a mathematical theory proof and analysis in four-dimensional game space. With the realistic decision-making processes of emissions firms linked in a unified model, the paper not only studies the effects of emission tax and debt to the collusive and output, but also gives an analysis of the optimal levels of debt and pollution abatement reversely.The conclusion has demonstrated that environmental regulations such as emission taxes may induce firms to alter their capital structure, which in turn influences both output levels and the effectiveness of the tax in controlling pollution emissions. After government decided the emission tax, debt of firms may facilitate collusion. Then firms maintain their profits cause they can't use the expansionary strategy. But this hurts the industry's competitiveness. With the existence of collusion in the market, the government raises the emission tax may lead tacit collusion more firmly. However, it is suggests that emission taxes may be more effective in lowering emissions in highly leveraged industries. In addition, emission taxes may act as a collusive device which reinforces the strategic commitment value of debt and induces firms to hold more debt in order to soften product market competition and get .higher profits.