Dynamic consistency of leader/fringe models of exhaustible resource markets

A dynamic feedback pricing model is developed for a leader/fringe supply market of exhaustible resources. The discrete game optimization model includes marginal costs which may be quadratic functions of cumulative production, a linear demand curve and variable length periods. The multiperiod formulation is based on the nesting of later periods' Kuhn-Tucker conditions into earlier periods' optimizations. This procedure leads to dynamically consistent solutions where the leader's strategy is credible as he has no incentive to alter his original plan at some later stage. A static leader-fringe model may yield multiple local optima. This can result in the leader forcing the fringe to produce at their capacity constraint, which would otherwise be non-binding if it is greater than the fringe's unconstrained optimal production rate. Conditions are developed where the optimal solution occurs at a corner where constraints meet, of which limit pricing is a special case. The 2-period leader/fringe feedback model is compared to the computationally simpler open-loop model. Under certain conditions, the open-loop model yields the same result as the feedback model. A multiperiod feedback model of the world oil market with OPEC as price-leader and the remaining world oil suppliers comprising the fringe is compared with the open-loop solution. The optimal profits and prices are very similar, but large differences in production rates may occur. The exhaustion date predicted by the open-loop model may also differ from the feedback outcome. Some numerical tests result in non-contiguous production periods for a player or limit pricing phases. 85 refs., 60 figs., 30 tabs