Note on the Open-Loop von Stackelberg Equilibrium in the Cartel Versus Fringe Model

Abstract

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Dynamic Games in the Economics of Natural Resources: A Survey

“…This was discussed in [147]. An interesting feature of the cartel-fringe model with an exhaustible resource is that there is a small subset of parameter values such that the open-loop Stackelberg solution is time-consistent [70,122,145].…”

Untitled

“…It makes a major difference how the equilibrium is precisely defined. If the open-loop equilibrium concept is employed then the phenomenon of dynamic inconsistency may occur (see Newbery 1981;Groot et al 1992), which makes the equilibrium concept obsolete, at least in the absence of binding contracts. The better equilibrium concept is the feedback von Stackelberg equilibrium, where time-inconsistency is ruled out by definition because the strategies of the players depend on the existing resource stocks.…”

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

“…A summary can be found in Section 3. However, this solution has the undesirable property that the optimal extraction path of the cartel is time-inconsistent for plausible values of the extraction costs and initial reserves (Ulph and Folie, 1981;Newbery, 1981;Ulph, 1982;Groot et al, 1992). Therefore, the next sections consider the feedback von Stackelberg solution.…”

“…For plausible values of the extraction costs and initial reserves, the strategy of the cartel proved to be time-inconsistent: the ex ante optimal extraction path ceases to be optimal ex post in case the strategy is reconsidered at a future point in time. This means that, in the absence of commitments, the cartel has an incentive to renege on the announced extraction path (Ulph and Folie, 1981;Newbery, 1981;Ulph, 1982;Groot et al, 1992). This problem attracted quite some attention (Karp and Newbery, 1991, 1993 but up to now the literature on exhaustible resources does not provide a time-consistent von Stackelberg solution for the cartel-versus-fringe model.…”