### Abstract

Original language | English |
---|---|

Pages (from-to) | 23-37 |

Journal | Journal of Mathematical Economics |

Volume | 45 |

Issue number | 1-2 |

Publication status | Published - 2009 |

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### Cite this

*Journal of Mathematical Economics*,

*45*(1-2), 23-37.

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*Journal of Mathematical Economics*, vol. 45, no. 1-2, pp. 23-37.

**Equilibria with coordination failures.** / Herings, P.J.J.; van der Laan, G.; Talman, A.J.J.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Equilibria with coordination failures

AU - Herings, P.J.J.

AU - van der Laan, G.

AU - Talman, A.J.J.

N1 - Appeared earlier as CentER Discussion Paper 2004-107

PY - 2009

Y1 - 2009

N2 - This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.

AB - This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.

M3 - Article

VL - 45

SP - 23

EP - 37

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 1-2

ER -