Strong Time-Consistency of a Core: An Application to the Pollution Control Problem in Eastern Siberia

Abstract

In this paper, we study the (strong) time-consistency property of the core for a linear-quadratic differential game of pollution control with nonzero absorption coefficient and real values of the model parameters. The values of parameters are evaluated based on the data for the largest aluminum enterprises of Eastern Siberia region of the Russian Federation for the year 2016. The obtained results are accompanied with illustrations.

Sustainable Optimal Control for Switched Pollution-Control Problem with Random Duration

“…All notations used through the paper are summarized in Appendix A, Table A1. In this study, we consider the optimal lake-pollution-control game model based on [15,16,18]. The game involves n players (factories).…”

“…The reasons behind this can be an equipment break-down, an economic failure. or a natural disaster, among many others [15]. In [15,16], differential pollution-control games with random duration were thoroughly analyzed.…”

“…or a natural disaster, among many others [15]. In [15,16], differential pollution-control games with random duration were thoroughly analyzed. However, the impact of seasonal fluctuation on the system was not considered.…”

Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations

“…The problem with asymmetry in different random time instants has been studied for some differential games in References [1,[51][52][53]. A similar cake-eating problem with different asymmetric discounting functions has been considered in Reference [54].…”

“…To this end, we use standard actuarial results and notation, and state a connection between the so-called actuarial equivalence principle (see Chapter 6 in Reference [57], Section on Premium Calculation, Nonlife in References [46,58]), and the feedback controllers found by means of the Dynamic Programming technique. We will end-up showing that, as in References [4,[27][28][29], the agents are willing to pay for the coverage of the insurance, in both: the one player context (see References [15,16]), and the game theoretic case with asymmetries (see References [1,[51][52][53]); where the unbalance comes from the choice of different fat-tailed distributions for the terminal times of extraction of the agents (see References [50,56,59]).…”