On a Nonrenewable Resource Extraction Game Played by Asymmetric Firms

Abstract

A differential game of extraction of a nonrenewable resource is taken into account, where two firms compete over time and their two terminal times of extraction are two different random variables. The winning firm will be the only one remaining in the game after the first one retires. We explicitly compute the Hamilton-Jacobi-Bellman equations of the model and solve them in an asymmetric game with logarithmic payoff structure and linear state dynamics. © 2013 Springer Science+Business Media New York

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

“…We are going to consider a simple model of common-property nonrenewable resource extraction published in [31] in 2000, and then further investigated in successive papers (e.g., [15,32]).…”

“…Recently, the notion of time consistency was extended to the case of discrete games (see, e.g., [14]). An extension of the time consistency problem to the case of differential games with random duration was first undertaken in [8], subsequently further investigation and results were accomplished in [15][16][17][18][19]. In [20], a random time horizon hybrid (see also [21] for a general treatment of hybrid differential games) differential game was considered such that the probability distribution can change over time.…”

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

“…then ξ(t 0 , x 0 , T) is a time-consistent imputation with IDP given by either (10) or (11). Also in this case, M = 1, that is we have a unique state variable x(t) indicating the stock of a nonrenewable resource at time t. The companies' strategic variables u i (t), for i = 1, .…”

“…If the 10 resource does not regenerate over time, such as natural gas or earth minerals, it is called exhaustible or 11 nonrenewable.…”

Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations

“…In this work we study an extension of the extraction game presented in Reference [1] to the case where the random terminal times follow (different) heavy-tailed distributions which are not necessarily compactly supported. We use the framework of the problem of common non-renewable resource exploitation as was posed in Reference [2], from both-the game-theoretical (cf.…”