Open-loop von Stackelberg equilibrium in the cartel-vs.-fringe model

Groot, F.; Withagen, Caam Cees; Zeeuw, AJ de

doi:10.1016/s0140-9883(99)00029-8

Cited by 12 publications

(6 citation statements)

References 16 publications

(7 reference statements)

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“…Finding the feedback equilibrium in this more complex setup would not only make our conclusions more realistic but also provide a contribution to the dynamic game literature through solving for a subgame-perfect Nash equilibrium with multiple state variables, one of which represents a fully exhaustible resource. Another interesting extension would be to introduce multiple oil exporters into the model, similar to [ 1 , 2 , 8 , 9 ]. Adding a fringe in addition to the cartel exporter is a better model of reality and would lead to interesting dynamics with the cartel and the fringe responding differently to the importer’s carbon tax.…”

Section: Discussionmentioning

confidence: 99%

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Battle for Climate and Scarcity Rents: Beyond the Linear-Quadratic Case

Kagan¹,

Ploeg

Withagen³

2015

Dyn Games Appl

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Industria imports oil, produces final goods and wishes to mitigate global warming. Oilrabia exports oil and buys final goods from the other country. Industria uses the carbon tax to impose an import tariff on oil and steal some of Oilrabia’s scarcity rent. Conversely, Oilrabia has monopoly power and sets the oil price to steal some of Industria’s climate rent. We analyze the relative speeds of oil extraction and carbon accumulation under these strategic interactions for various production function specifications and compare these with the efficient and competitive outcomes. We prove that for the class of HARA production functions, the oil price is initially higher and subsequently lower in the open-loop Nash equilibrium than in the efficient outcome. The oil extraction rate is thus initially too low and in later stages too high. The HARA class includes linear, loglinear and semi-loglinear demand functions as special cases. For non-HARA production functions, Oilrabia may in the open-loop Nash equilibrium initially price oil lower than the efficient level, thus resulting in more oil extraction and climate damages. We also contrast the open-loop Nash and efficient outcomes numerically with the feedback Nash outcomes. We find that the optimal carbon tax path in the feedback Nash equilibrium is flatter than in the open-loop Nash equilibrium. It turns out that for certain demand functions using the carbon tax as an import tariff may hurt consumers’ welfare as the resulting user cost of oil is so high that the fall in welfare wipes out the gain from higher tariff revenues.

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Section: Discussionmentioning

confidence: 99%

“… 4 Groot et al [ 8 ] show that the open-loop Stackelberg equilibrium outcome may give rise to discontinuities in the equilibrium price trajectory. Groot et al [ 9 ] derive the feedback Stackelberg equilibrium outcome for the cartel–fringe model.…”

mentioning

confidence: 99%

Battle for Climate and Scarcity Rents: Beyond the Linear-Quadratic Case

Kagan¹,

Ploeg

Withagen³

2015

Dyn Games Appl

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“…The second effect works in the opposite direction. In this case, the cartel would like to announce ambitious output targets so as to pre-empt supply by the non-OPEC fringe, even when such a strategy would not be credible ex-post (Groot et al, 2000(Groot et al, , 2003.…”

Section: Methodsmentioning

confidence: 99%

Imperfect Cartelization in OPEC

Okullo

Reynès

2016

SSRN Journal

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A model of global oil production is applied to study cartelization by OPEC countries. Writing out the shadow price on quota allocations so as to draw correspondence to coefficients of cooperation (Cyert et al. 1973), we examine the incentives that different OPEC members to collude. We find that heterogeneity in OPEC and the supplies of the non-OPEC fringe create strong incentives against OPEC cooperation. OPEC's optimal supply strategy although observed to be substantially more restrictive than that of a Cournot-Nash oligopoly, is found to still be more accommodative than that of a perfect cartel. The strategy involves allocating larger than proportionate quotas to smaller and relatively costlier producers as if to bribe their participation in the cartel. This is contrary to predictions of the standard cartel model that such producers should be allocated relatively more stringent quotas.Furthermore, we find that cartel collusion is likely to be sustained for elastic than inelastic demand. Since global oil demand is well known to be inelastic, this observation provides another structural explanation for why OPEC behavior is inconsistent with that of a perfect cartel. Our study points to multiple headwinds that limit OPECs ability to raise long-run global oil prices.

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“…. In (8), we have shown that the open-loop Nash equilibrium tax is the Pigouvian tax which evolves according to τ = ρτ − D (E 0 + S 0 − S). Hence, we get the dynamics of the producer price of oil:…”

Section: Case: Iso-elastic Oil Demandmentioning

confidence: 99%