Differential games of exhaustible resource extraction

This thesis is concerned with game-theoretic models of oligopoly resource markets. They revolve around an open market, on which a number of firms sell a common resource. The market price-demand relationship means that the price (demand) that results from the firm’s production (pricing) decisions is a function of the decisions of all firms selling to that market. This means that firms must generally anticipate the actions of competing firms when determining their own strategies, which means that these models often need to be analysed using game theory. We focus on games in which the resource is exhaustible, with the exception of Chapter 5, in which the majority of the analysis is carried out in an inexhaustible resources setting. Exhaustibility introduces an additional complication into these games; that of allocating the extraction and sale of a limited resource pool over time. We consider several separate areas of extension, which we outline below. In Chapter 2, we consider a dynamic Stackelberg game. Stackelberg competition is an asymmetric form of competition in which one player (the leader) has the ability to pre-commit to and announce a strategy in advance. The ability to pre-commit to a strategy is almost always highly valuable, and in this case allows the leader to drive down the follower’s production by pre-committing to drive up their own. We follow the framework used in [62] to analyse Cournot competition to derive our results. In Chapter 3, we compare the two settings in which resource extraction models are usually formulated: Open-Loop, in which the players determine their strategies as functions of time and the initial resource levels of the players only; and Feedback-Loop, in which the players determine their strategies at each point in time as a function of the current resource levels at that time. Our focus is on the investigation of the relationship between the difference in the production or value of a firm under these two models, and the distribution of resources across the firms. In Chapter 4, we consider a common property resource game. These involve multiple firms which can extract from a common resource pool. We study a widely-used Open- viii Loop model, as formulated in [79]. We examine the result that analysis of the problem by standard methods results in two candidate equilibria, and argue that one of these equilibria can be ruled out by construction of a superior response. In Chapter 5, we analyse joint constraints on production, namely constraints which are met when the total production is above or below a certain level. It is a well- established result that these constraints can result in multiple equilibria. We provide several brief extensions to existing uniqueness results. We also demonstrate methods by which these results can be utilised to analyse games with piecewise-linear windfall taxes or congestion charges. Finally, we discuss the problems of extending these results to games with resource exhaustibility.