Strong Time Consistency Research Articles

Strong time-consistency in the cartel-versus-fringe model

Due to developments on the oil market in the 1970s, the theory of exhaustible resources was extended with the cartel-versus-fringe model to characterize markets with one big coherent cartel and a large number of small suppliers called the fringe. Because cartel and fringe are leader and follower, the von Stackelberg solution concept is appropriate for the supply side of this market. The solution for the cartel-versus-fringe model, presented in the previous literature, proved to be time-inconsistent for a large plausible range of values for extraction costs and initial reserves. This paper provides a (strongly) time-consistent solution for the cartel-versus-fringe model.

Strong Time-Consistency in the Cartel-Versus-Fringe Model

Strong Time-Consistency in the Cartel-Versus-Fringe Model

Iterative computation of noncooperative equilibria in nonzero-sum differential games with weakly coupled players

We study the Nash equilibria of a class of two-person nonlinear, deterministic differential games where the players are weakly coupled through the state equation and their objective functionals. The weak coupling is characterized in terms of a small perturbation parameter e. With e=0, the problem decomposes into two independent standard optimal control problems, while for e≠0, even though it is possible to derive the necessary and sufficient conditions to be satisfied by a Nash equilibrium solution, it is not always possible to construct such a solution. In this paper, we develop an iterative scheme to obtain an approximate Nash solution when e lies in a small interval around zero. Further, after requiring strong time consistency and/or robustness of the Nash equilibrium solution when at least one of the players uses dynamic information, we address the issues of existence and uniqueness of these solutions for the cases when both players use the same information, either closed loop or open loop, and when one player uses open-loop information and the other player uses closed-loop information. We also show that, even though the original problem is nonlinear, the higher (than zero) order terms in the Nash equilibria can be obtained as solutions to LQ optimal control problems or static quadratic optimization problems.