Essays in Game Theory and Forest Economics


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Virginia Tech


This dissertation consists of three essays in theoretical and applied microeconomics: the first essay is in cooperative game theory, and the second and third essays relate to forest economics. The first chapter studies a class of cooperative games dubbed ``r-essential games''. Cooperative game theory has proposed different notions of powerful players. For example, big-boss games (Muto et al., 1988) and clan games (Potters et al., 1989) are particular cases of veto games (Bahel, 2016). The first chapter extends these veto games by assuming that there is a given subset of powerful (or essential) players, but only a few (as opposed to all) essential players are required for a coalition to have a positive value. The resulting games, which are called r-essential games, encompass convex games (Shapley, 1971) and veto games. We show that r-essential games have a nonempty core. We give a recursive description of the core. Moreover, it is shown that the core and the bargaining set are equivalent for every r-essential game. An application to networks is provided. The second chapter employs a two-principal, one-agent model to estimate the social cost of fiscal federalism in China's northeast native forests. China's key forested region is located in the northeast and consists of state forest enterprises which manage forest harvesting and reforestation. Deforestation is a major problem there and has resulted in several central government reforms. We develop a framework for assessing the social cost of state forest enterprise deforestation. We first develop a two-principal, one-agent model that fits the federalistic organization of state forests, in that state forest managers make (potentially hidden) decisions under influence of provincial and central government policies. This model is used to quantify the social cost of these hidden actions. We then use panel data from a survey conducted by Peking University to compute social welfare losses and to formally identify the main factors in these costs. A sensitivity analysis shows that, interestingly, command and control through lower harvesting limits and a more accurate monitoring system are more important to lowering social welfare losses than conventional incentives targeting the wages of forest managers. Through regression analysis we also find that the more remote areas with a higher percentage of mature natural forests are the ones that will always have the highest social welfare losses. The third chapter studies the problem of choosing a rotation under uncertain future ecosystem values and timber prices. This problem is nearly as old as the field of forest economics itself. A forest owner faces various uncertainties caused by climate change and market shocks, due to its long-term nature of production and the joint production of interrelated timber and amenity (non-harvesting) benefit streams. The vast literature in stochastic rotation problems simply assumes a known probability distribution for whatever parameter is uncertain, but this type of assumption may lead to misspecification of a rotation decision model if a forest owner has no such information. We study a more relevant question of how to choose rotation ages when there is pure (or Knightian) uncertainty, in that the forest owner does not know distributional features of parameters and further can be averse to this type of information deficit. This chapter is the first to investigate pure uncertainty in amenity benefit streams and is also the first to analytically solve a stochastic rotation problem under pure uncertainty in either amenity streams or market prices. We use robust methods developed in macroeconomics that are particularly suited to forest capital investment problem, but with important differences owing to the nature of forest goods production. The results show that newer models suggesting rotation ages could be longer under volatile parameter distributions do not hold generally when pure uncertainty and forest owner uncertainty aversion is considered. Rather, the earlier literature showing faster or greater harvesting with increases in risk under risk neutrality may actually be a more general result than current literature supposes. In particular, we find that a landowner tends to harvest more when his degree of uncertainty aversion is higher and the model is misspecified by assumption, or when the volatility of an uncertain process is higher. These situations tend to magnify model misspecification costs, especially because the forest manager always assumes the worst case will happen when there is uncertainty. This implies the decision maker is pessimistic in the sense that he or she is always trying to maximize the utility under the worst possible state of nature (the lowest amenity benefit or the lowest timber price). Whether landowners are in fact uncertainty averse and assume the worst case in their decisions remains to be empirically investigated, but our work suggests it is an important question that must be answered.



TU game, r-essential, core, objection, network, deforestation, two-principal-one-agent model, social welfare loss, fiscal federalism, climate change, pure uncertainty, robust control, stochastic dynamic programming